Example 1 · level 1
Two angles of a triangle are 41° and 57°. Find the third angle (in degrees).
Show solution
- 41° + 57° = 98°.
- Third angle = 180° − 98° = 82°.
Answer: 82
CLASS 7 MATHS · THE TRIANGLE AND ITS PROPERTIES
Angle sum and exterior angle of a triangle
The three angles of a triangle add to 180°. An exterior angle equals the sum of the two interior opposite angles.
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Worked examples
Example 2 · level 2
In triangle ABC, ∠A = 60° and ∠B = 21°. Side BC is extended to D. Find the exterior angle ∠ACD (in degrees).
Show solution
- ∠ACD = ∠A + ∠B = 60° + 21° = 81°.
- (Check: ∠C = 99°, and 99° + 81° = 180° on the straight line.)
Answer: 81
Example 3 · level 3
The angles of a triangle are in the ratio 2 : 7 : 6. Find the smallest angle (in degrees).
Show solution
- 15x = 180 → x = 12.
- Angles: 24°, 84°, 72°.
- Smallest = 24°.
Answer: 24