Angles and Triangles

A Today you'll learn

Classify angles as acute, right, obtuse, straight, and reflex.
Classify triangles by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse).
Verify and apply the Triangle Angle Sum Property (sum of all interior angles = 180°).

B Let's understand

∠A (60°) + ∠B (60°) + ∠C (60°) = 180°

Triangle Angle Sum Property: Interior angles always add up to 180°.

An angle is formed when two rays meet at a common endpoint called the vertex, measured in degrees (°). Angles are classified by their measure: Acute (between 0° and 90°), Right (exactly 90°), Obtuse (between 90° and 180°), Straight (exactly 180°), and Reflex (between 180° and 360°). A triangle is a 3-sided polygon. By sides, triangles are Equilateral (all 3 sides equal), Isosceles (2 sides equal), or Scalene (no sides equal). Crucially, the sum of all three interior angles in any triangle always equals 180°.

C See it step by step

Example 1: Classify the angle measuring 115° and 72°.

Step 1: 115° is greater than 90° and less than 180°, so it is an Obtuse angle.
Step 2: 72° is greater than 0° and less than 90°, so it is an Acute angle.

Example 2: In triangle ABC, angle A = 65° and angle B = 50°. Find angle C.

Step 1: The sum of all angles in a triangle is 180°: angle A + angle B + angle C = 180°.
Step 2: Add known angles: 65° + 50° = 115°.
Step 3: Subtract from 180°: angle C = 180° - 115° = 65°.
Step 4: Since two angles are 65°, triangle ABC is also an Isosceles triangle.

D Your turn

What is the sum of the angles in any triangle?

Look back at "Let's understand" above for a clue.

E Ready to practise?

Key idea 1

A right angle measures exactly 90°; a straight angle measures exactly 180°.

Key idea 2

Acute angles are < 90°; obtuse angles are between 90° and 180°.

Key idea 3

Equilateral triangles have 3 equal sides and three 60° angles.

Key idea 4

Isosceles triangles have 2 equal sides and 2 equal opposite angles.

Key idea 5

The sum of the three interior angles of any triangle is always 180°.

Warm up

1. Name the type of angle: 45°.

2. Name the type of angle: 90°.

3. Name the type of angle: 135°.

Practise

4. Name the type of triangle where all three sides are equal.

5. Two angles of a triangle are 70° and 50°. Find the third angle.

6. Can a triangle have angles measuring 60°, 70°, and 80°? Explain why or why not.

Challenge

7. In a right-angled triangle, one acute angle is 35°. Find the other acute angle.

8. A triangle has side lengths 7 cm, 7 cm, and 10 cm. Name the triangle based on its sides.

Download worksheet (PDF)

Question 1: Name the type of angle: 45°.

Answer: Acute angle

Question 2: Name the type of angle: 90°.

Answer: Right angle

Question 3: Name the type of angle: 135°.

Answer: Obtuse angle

Question 4: Name the type of triangle where all three sides are equal.

Answer: Equilateral triangle

Question 5: Two angles of a triangle are 70° and 50°. Find the third angle.

Answer: 60° (since 180° - 120° = 60°)

Question 6: Can a triangle have angles measuring 60°, 70°, and 80°? Explain why or why not.

Answer: No, because 60° + 70° + 80° = 210°, which exceeds 180°

Question 7: In a right-angled triangle, one acute angle is 35°. Find the other acute angle.

Answer: 55° (since 90° - 35° = 55°)

Question 8: A triangle has side lengths 7 cm, 7 cm, and 10 cm. Name the triangle based on its sides.

Answer: Isosceles triangle