Sum of exterior angles of any polygon is?

360° — walking around turns a full circle.

Which is not a polygon?

Circle — has no straight sides.

Cylinder — has height and circular faces.

Co-Ordinate Geometry Class 10

Q: What is the sum of the interior angles of a triangle?

180° — In any triangle the interior angles add up to 180°.

Q: Area of a square with side length 5 cm?

25 cm² — area = side × side.

Q: Perimeter of a rectangle 4 cm × 6 cm?

20 cm — perimeter = 2×(length+width).

Q: A right triangle has legs 3 and 4. Hypotenuse is?

5 — by Pythagoras: √(3²+4²)=5.

Q: How many lines of symmetry has an equilateral triangle?

3 — medians are symmetry lines.

Q: The diameter of a circle is 10 cm. Its radius is?

5 cm — radius = diameter ÷ 2.

Q: If two angles are complementary, their sum is:

90° — complementary angles add to 90°.

Q: If two angles are supplementary, they add to:

180° — supplementary angles add to 180°.

Q: Area of triangle with base 10 cm and height 6 cm?

30 cm² — area = ½×base×height.

Q: Which shape has all opposite sides parallel?

Parallelogram — both pairs of opposite sides are parallel.

Introduction to Co-ordinate Geometry class 10
Coordinate Geometry (also called Cartesian Geometry) is the branch of mathematics that combines algebra and geometry using a system of coordinates. It allows us to represent points, lines, and shapes on a plane using ordered pairs �.
In Class 10, Coordinate Geometry mainly deals with:
Plotting points on the Cartesian plane.
Finding the distance between two points.
Finding the midpoint of a line segment.
Calculating the slope and equation of a line.
Dividing a line segment in a given ratio (section formula).
This chapter of co-ordinate geometry class 10 is important because it provides tools to solve real-life problems involving locations, maps, navigation, and design. It also builds the foundation for higher-level mathematics like calculus and vector geometry.

geometry — 50 Interactive MCQs for co-ordinate geometry class 10 Exams

Kid friendly, step-by-step solutions. Click an option and press Check.

Use Check to reveal correct answer and a step-by-step solution. All questions are about co-ordinate geometry class 10.

Q1 What is the sum of the interior angles of a triangle?

topic: geometry basics

A) 90° B) 180° C) 360° D) 270°

Step-by-step solution (triangle — geometry)

Take any triangle and draw a line parallel to one side through the opposite vertex.
This creates corresponding angles that add up to a straight line, 180°.
Therefore, the three interior angles always add to 180°.

Q2 Area of a square with side length 5 cm?

geometry area

A) 10 cm² B) 15 cm² C) 25 cm² D) 20 cm²

Steps (area of square — geometry)

Formula: area = side × side.
Side = 5 cm → area = 5 × 5 = 25 cm².

Q3 Perimeter of a rectangle 4 cm × 6 cm?

geometry perimeter

A) 20 cm B) 24 cm C) 10 cm D) 12 cm

Steps (perimeter — geometry)

Perimeter = 2×(length + width) = 2×(6 + 4) = 2×10.
2×10 = 20 cm.

Q4 What is the area of a circle with radius 7 cm? (Use π = 22/7)

geometry circle

A) 77 cm² B) 154 cm² C) 49 cm² D) 154π cm²

Steps (area of circle — geometry)

Formula: area = πr². r = 7.
Using π = 22/7: area = (22/7)×7×7 = 22×7 = 154 cm².

Q5 A right triangle has legs 3 and 4. Hypotenuse is?

geometry right triangle

A) 5/2 B) 6 C) 5 D) 7

Steps (Pythagoras — geometry)

Hypotenuse² = 3² + 4² = 9 + 16 = 25.
Hypotenuse = √25 = 5.

Q6 How many lines of symmetry has an equilateral triangle?

geometry symmetry

A) 3 B) 1 C) 0 D) 6

Steps (symmetry — geometry)

Equilateral triangle has 3 equal sides and 3 equal angles.
Each line from a vertex to the midpoint of opposite side is a symmetry line → total 3.

Q7 What is the measure of each angle in an equilateral triangle?

geometry angles

A) 60°, 30°, 90° B) 45°, 45°, 90° C) 30°, 60°, 90° D) 60°, 60°, 60°

Steps (angles — geometry)

Sum of angles in triangle = 180°.
Equilateral: all three equal → each = 180° ÷ 3 = 60°.

Q8 The diameter of a circle is 10 cm. Its radius is?

geometry radius

A) 10 cm B) 5 cm C) 20 cm D) 2 cm

Steps (radius — geometry)

Radius = diameter ÷ 2 = 10 ÷ 2 = 5 cm.

Q9 If two angles are complementary, their sum is:

geometry angles

A) 90° B) 180° C) 360° D) 45°

Steps (complementary — geometry)

By definition, complementary angles add to 90°.

Q10 If two angles are supplementary, they add to:

geometry angles

A) 90° B) 270° C) 180° D) 360°

Steps (supplementary — geometry)

By definition, supplementary angles add to 180°.

Q11 Area of triangle with base 10 cm and height 6 cm?

geometry area triangle

A) 60 cm² B) 30 cm² C) 16 cm² D) 100 cm²

Steps (triangle area — geometry)

Formula: area = ½ × base × height = 0.5 × 10 × 6.
0.5 × 10 × 6 = 5 × 6 = 30 cm².

Q12 Which shape has all opposite sides parallel?

geometry quadrilateral

A) Parallelogram B) Trapezoid C) Kite D) Triangle

Steps (parallelogram — geometry)

Definition: parallelogram = both pairs of opposite sides are parallel.
Thus the correct shape is parallelogram.

Q13 A regular hexagon has how many sides?

geometry polygons

A) 5 B) 4 C) 7 D) 6

Steps (hexagon — geometry)

Prefix “hexa” means 6 → hexagon has 6 sides.

Q14 Sum of exterior angles (one at each vertex) of any polygon is?

geometry polygons

A) Depends on polygon B) 360° C) 180° D) 720°

Steps (exterior angles — geometry)

Exteriors around the polygon turn a full circle when walked around → total = 360°.

Q15 If a circle’s circumference is 31.4 cm and π = 3.14, radius is?

geometry circle circumference

A) 2.5 cm B) 3 cm C) 5 cm D) 10 cm

Steps (circumference — geometry)

Circumference = 2πr → 31.4 = 2×3.14×r.
2×3.14 = 6.28. So r = 31.4 ÷ 6.28 = 5 → 5 cm.

Q16 Which pair of angles are always equal in isosceles triangle?

geometry isosceles

A) Base angles B) Vertex and base angle C) All three different D) None

Steps (isosceles — geometry)

Isosceles triangle has two equal sides; angles opposite those sides are equal.
Those equal angles are the two base angles → base angles.

Q17 What is the volume of a cube with side 3 cm?

geometry volume

A) 6 cm³ B) 27 cm³ C) 9 cm³ D) 18 cm³

Steps (cube volume — geometry)

Volume of cube = side³ = 3×3×3 = 27 cm³.

Q18 Diagonal of a square with side 1 cm is?

geometry diagonal

A) 1 cm B) 2 cm C) √3 cm D) √2 cm

Steps (diagonal — geometry)

Diagonal d = side × √2 = 1 × √2 = √2 cm.

Q19 What shape has exactly one pair of parallel sides?

geometry trapezoid

A) Trapezoid (trapezium) B) Rectangle C) Parallelogram D) Square

Steps (trapezoid — geometry)

A trapezoid has only one pair of opposite sides parallel → answer is trapezoid.

Q20 If angle A is 50° and angle B is 60° in a triangle, angle C is?

geometry triangle angles

A) 60° B) 70° C) 70° D) 80°

Steps (triangle sum — geometry)

Sum = 180°. So C = 180 − (50 + 60) = 180 − 110 = 70°.

Q21 Which solid has 6 faces, 12 edges and 8 vertices?

geometry solids

A) Tetrahedron B) Cube (hexahedron) C) Cylinder D) Sphere

Steps (solid shapes — geometry)

Cube has 6 square faces, 12 edges and 8 corners (vertices) → cube.

Q22 A line that touches a circle at exactly one point is called?

geometry tangent

A) Tangent B) Secant C) Chord D) Radius

Steps (tangent — geometry)

Definition: tangent touches circle at exactly one point → answer tangent.

Q23 Chord of a circle is a line segment that:

geometry chord

A) Passes through center B) Is outside circle C) Joins two points on the circle D) Tangent at a point

Steps (chord — geometry)

Chord joins any two points on the circle → joins two points on the circle.

Q24 Which angle is formed when two rays share a common endpoint?

geometry angle definitions

A) Reflex angle B) Straight angle C) Exterior angle D) An angle (general)

Steps (angle definition — geometry)

Two rays from a common endpoint form an angle — generically called an angle.

Q25 The longest chord of a circle is called:

geometry diameter

A) Tangent B) Diameter C) Radius D) Secant

Steps (diameter — geometry)

Diameter passes through center and has endpoints on circle — it’s the longest chord → diameter.

Q26 If two chords are equal in a circle, then their arcs are:

geometry arcs

A) Equal B) Complementary C) Supplementary D) Unrelated

Steps (equal chords — geometry)

Equal chords subtend equal arcs in the same circle → arcs are equal.

Q27 Interior angles of a regular pentagon each measure?

geometry regular polygon

A) 90° B) 108° C) 120° D) 72°

Steps (regular pentagon — geometry)

Sum interior = (n−2)×180 = 3×180 = 540°. For n=5 equal angles → 540 ÷ 5 = 108°.

Q28 Which is NOT a property of rectangles?

geometry rectangle

A) Opposite sides equal B) All angles 90° C) All sides equal D) Opposite sides parallel

Steps (rectangle properties — geometry)

Rectangle has opposite sides equal, angles 90°, opposite sides parallel. Not all sides equal (that’s a square) → All sides equal is NOT true.

Q29 Which is the shortest distance between two points?

geometry shortest path

A) A straight line B) A curve C) A broken line D) A circle arc

Steps (shortest path — geometry)

From Euclidean geometry: shortest path between two points is a straight line → straight line.

Q30 Which of the following is not a polygon?

geometry polygon

A) Triangle B) Rectangle C) Pentagon D) Circle

Steps (polygon vs circle — geometry)

Polygons are made of straight sides. Circle has no straight sides → so circle is NOT a polygon.

Q31 Which of these is a 3D shape?

geometry 3D

A) Square B) Cylinder C) Triangle D) Rectangle

Steps (3D shapes — geometry)

Cylinder has height and circular faces → it’s 3D; others are flat (2D) → cylinder.

Q32 What is the midpoint of segment from (0,0) to (4,6)?

geometry coordinate

A) (2, 3) B) (4, 6) C) (1, 2) D) (0, 0)

Steps (midpoint — geometry)

Midpoint = ((x1+x2)/2, (y1+y2)/2) = ((0+4)/2, (0+6)/2) = (2,3).

Q33 Which triangle has all sides different?

geometry scalene

A) Isosceles B) Scalene C) Equilateral D) Right triangle

Steps (scalene — geometry)

Scalene triangle: no sides equal → scalene.

Q34 If one interior angle of a regular octagon is x, x = ?

geometry regular octagon

A) 120° B) 135° C) 135° D) 150°

Steps (regular octagon — geometry)

Sum interior = (8−2)×180 = 6×180 = 1080°; each = 1080 ÷ 8 = 135° → 135°.

Q35 Which is true for parallel lines?

geometry parallel

A) They never meet B) They meet at infinity C) They meet at one point D) They are perpendicular

Steps (parallel lines — geometry)

Parallel lines are defined as lines in the same plane that do not meet → they never meet.

Q36 The centre of gravity of a uniform triangular lamina lies at:

geometry centroid

A) Circumcentre B) Orthocentre C) Centroid (intersection of medians) D) Incentre

Steps (centroid — geometry)

Centroid is intersection of medians, and it is center of mass for uniform triangle → centroid.

Q37 Area of a parallelogram with base 8 and height 3?

geometry parallelogram

A) 11 B) 24 C) 32 D) 8

Steps (parallelogram area — geometry)

Area = base × height = 8 × 3 = 24.

Q38 A diameter divides a circle into two parts called?

geometry semicircle

A) Semicircles B) Sectors C) Arcs D) Chords

Steps (semicircle — geometry)

Diameter splits circle into two equal halves called semicircles.

Q39 A sector of a circle is:

geometry sector

A) A chord B) A tangent C) A ‘pizza slice’ bounded by two radii and an arc D) The center

Steps (sector — geometry)

Sector is region between two radii and the arc joining them — like a pizza slice → pizza slice.

Q40 The perpendicular from the center to a chord bisects the chord. True or false?

geometry perpendicular

A) False B) True C) Only if chord passes through center D) Depends on circle

Steps (perpendicular to chord — geometry)

Perpendicular from center to a chord meets it at its midpoint—so it bisects the chord → True.

Q41 If two lines are perpendicular, their slopes (in coordinate plane) multiply to?

geometry coordinates

A) −1 B) 0 C) 1 D) Undefined

Steps (perpendicular slopes — geometry)

In coordinate geometry, slopes m1×m2 = −1 if lines are perpendicular → product = −1.

Q42 If ∠1 = 40° and ∠2 is vertically opposite, ∠2 = ?

geometry vertically opposite

A) 50° B) 40° C) 140° D) 90°

Steps (vertically opposite angles — geometry)

Vertically opposite angles formed by intersecting lines are equal → so ∠2 = 40°.

Q43 Which is a right prism?

geometry prism

A) Cylinder-like shape with polygon bases and straight sides B) Cone C) Pyramid D) Sphere

Steps (prism — geometry)

Prism has two parallel congruent polygonal bases and straight lateral edges → option A describes a prism-like object → A.

Q44 Interior angle of a regular triangle (equilateral) is?

geometry h3: triangle geometry

A) 30° B) 45° C) 90° D) 60°

Steps (equilateral triangle — geometry)

Equilateral has all equal angles: 180 ÷ 3 = 60°.

Q45 Area of a right triangle with legs 6 and 8?

geometry pythagoras area

A) 48 B) 28 C) 24 D) 14

Steps (right triangle area — geometry)

Area = ½ × leg1 × leg2 = 0.5 × 6 × 8 = 3 × 8 = 24.

Q46 Which statement about a circle’s radius is true?

geometry radius center

A) Radius = diameter B) Radius is half the diameter C) Radius is twice the diameter D) Radius equals circumference

Steps (radius vs diameter — geometry)

Diameter = 2×radius, so radius = diameter ÷ 2 → radius is half the diameter.

Q47 What do you call a 4-sided polygon?

geometry quadrilateral

A) Quadrilateral B) Triangle C) Pentagon D) Hexagon

Steps (four-sided — geometry)

Quad = four; quadrilateral = four-sided polygon → quadrilateral.

Q48 If one exterior angle of a regular pentagon is 72°, interior is?

geometry exterior interior

A) 90° B) 60° C) 108° D) 72°

Steps (exterior-interior — geometry)

Interior + exterior at a vertex = 180°. So interior = 180 − 72 = 108°.

Q49 Which is a right angle?

geometry right angle

A) 90° B) 45° C) 60° D) 180°

Steps (right angle — geometry)

Right angle equals 90°.

Q50 If a scale factor of similar shapes is 2, the area scale factor is?

geometry similarity

A) 2 B) 4 C) 8 D) 16

Steps (scale factor — geometry)

Area scale factor = (linear scale factor)² = 2² = 4.

End of geometry MCQs — practice and review steps to build confidence!

practice more MCQs on Mathematics here