Geometry MCQs – Angles, Triangles, Circles & Area
Practice 10 MCQs on geometry covering angles, types of triangles, circle theorems, area and perimeter formulas, and Pythagoras’ theorem.
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Q1
The sum of angles in a triangle is always:
✓ B – 180°
The sum of all interior angles in any triangle is always 180°. This is a fundamental theorem of Euclidean geometry. For a right triangle: 90° + two other angles = 180°.
The sum of all interior angles in any triangle is always 180°. This is a fundamental theorem of Euclidean geometry. For a right triangle: 90° + two other angles = 180°.
Q2
What is the area of a rectangle with length 8 cm and width 5 cm?
✓ B – 40 cm²
Area of rectangle = length × width = 8 × 5 = 40 cm². Perimeter = 2(l + w) = 2(8+5) = 26 cm. Always distinguish between area (cm²) and perimeter (cm).
Area of rectangle = length × width = 8 × 5 = 40 cm². Perimeter = 2(l + w) = 2(8+5) = 26 cm. Always distinguish between area (cm²) and perimeter (cm).
Q3
In a right-angled triangle, the side opposite the right angle is called:
✓ C – Hypotenuse
The hypotenuse is the longest side of a right triangle, opposite the 90° angle. Pythagoras’ Theorem: a² + b² = c² where c is the hypotenuse.
The hypotenuse is the longest side of a right triangle, opposite the 90° angle. Pythagoras’ Theorem: a² + b² = c² where c is the hypotenuse.
Q4
The formula for the area of a circle is:
✓ B – πr²
Area of circle = πr² where r is the radius. Circumference = 2πr or πd. Remember: area uses r² while circumference uses r (or d). π ≈ 3.14159.
Area of circle = πr² where r is the radius. Circumference = 2πr or πd. Remember: area uses r² while circumference uses r (or d). π ≈ 3.14159.
Q5
A triangle with all three sides equal is called:
✓ C – Equilateral
An equilateral triangle has all 3 sides equal and all 3 angles equal (60° each). Isosceles = 2 equal sides. Scalene = no equal sides. Right-angled = one 90° angle.
An equilateral triangle has all 3 sides equal and all 3 angles equal (60° each). Isosceles = 2 equal sides. Scalene = no equal sides. Right-angled = one 90° angle.
Q6
What is the value of the hypotenuse if the two legs of a right triangle are 3 cm and 4 cm?
✓ A – 5 cm
c² = a² + b² = 3² + 4² = 9 + 16 = 25 → c = √25 = 5 cm. This is the famous 3-4-5 Pythagorean triple — memorize it! Other triples: 5-12-13, 8-15-17.
c² = a² + b² = 3² + 4² = 9 + 16 = 25 → c = √25 = 5 cm. This is the famous 3-4-5 Pythagorean triple — memorize it! Other triples: 5-12-13, 8-15-17.
Q7
The angle in a semicircle is always:
✓ C – 90°
The angle in a semicircle is always 90° (Thales’ Theorem). Any angle inscribed in a semicircle — where the diameter is the chord — will be a right angle.
The angle in a semicircle is always 90° (Thales’ Theorem). Any angle inscribed in a semicircle — where the diameter is the chord — will be a right angle.
Q8
What is the sum of exterior angles of any polygon?
✓ C – 360°
The sum of exterior angles of any convex polygon is always 360°, regardless of the number of sides. This is a universal geometric theorem. Each exterior angle of a regular n-gon = 360°/n.
The sum of exterior angles of any convex polygon is always 360°, regardless of the number of sides. This is a universal geometric theorem. Each exterior angle of a regular n-gon = 360°/n.
Q9
The perimeter of a square with side 6 cm is:
✓ B – 24 cm
Perimeter of square = 4 × side = 4 × 6 = 24 cm. Area of square = side² = 36 cm². Always distinguish: perimeter is total boundary length (linear), area is the space enclosed (squared units).
Perimeter of square = 4 × side = 4 × 6 = 24 cm. Area of square = side² = 36 cm². Always distinguish: perimeter is total boundary length (linear), area is the space enclosed (squared units).
Q10
Two angles are supplementary if their sum equals:
✓ B – 180°
Supplementary angles sum to 180°. Complementary angles sum to 90°. Angles on a straight line are supplementary. Vertically opposite angles are equal.
Supplementary angles sum to 180°. Complementary angles sum to 90°. Angles on a straight line are supplementary. Vertically opposite angles are equal.
About These Geometry MCQs
These Geometry MCQs cover angles, triangles, circles, area and perimeter formulas, and Pythagoras’ theorem. Ideal for Class 8–10 students and board exam preparation.
Geometry is a core component of mathematics exams. These questions strengthen understanding of shapes, theorems, and calculations with detailed step-by-step explanations.
Topics Covered
- Angle sum in triangles and polygons
- Types of triangles — equilateral, isosceles, scalene
- Pythagoras’ theorem — a² + b² = c²
- Area and perimeter formulas (rectangle, circle, square)
- Circle theorems — angle in semicircle
- Supplementary and complementary angles
Geometry Exam Tips
Memorize all area and perimeter formulas on a single sheet. For Pythagoras, practice the common triples (3-4-5, 5-12-13). Always draw a diagram when solving geometry problems — it prevents silly mistakes.
Frequently Asked Questions
What is Pythagoras’ Theorem? ›
Pythagoras’ Theorem states that in a right-angled triangle, c² = a² + b², where c is the hypotenuse (longest side). Common Pythagorean triples: 3-4-5, 5-12-13, 8-15-17.
What is the difference between complementary and supplementary angles? ›
Complementary angles sum to 90°. Supplementary angles sum to 180°. Memory tip: C comes before S alphabetically, and 90 comes before 180.
What are the properties of an equilateral triangle? ›
An equilateral triangle has 3 equal sides, 3 equal angles (60° each), 3 lines of symmetry, and all perpendicular bisectors/medians meet at the centroid.
What is the angle in a semicircle? ›
The angle in a semicircle is always 90° (Thales’ Theorem). If AB is a diameter and C is any point on the semicircle, then angle ACB = 90°.
What is the sum of interior angles of a polygon? ›
Sum = (n−2) × 180°, where n is the number of sides. Triangle: 180°, Quadrilateral: 360°, Pentagon: 540°, Hexagon: 720°.
