The sum of the three interior angles of a triangle is always 180°. Also, one exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.
Example ①
In △ABC, ∠A=50° and ∠B=70°. Find ∠C.
Answer: ∠C = 180°−50°−70° = 60°
In △ABC, ∠A=50° and ∠B=70°. Find ∠C.
Answer: ∠C = 180°−50°−70° = 60°
Example ② (Exterior Angles)
In △ABC, ∠A=45° and ∠B=75°. Find the exterior angle at vertex C.
Answer: Exterior angle = ∠A + ∠B = 45°+75° = 120°
In △ABC, ∠A=45° and ∠B=75°. Find the exterior angle at vertex C.
Answer: Exterior angle = ∠A + ∠B = 45°+75° = 120°
Key Points
- Sum of the interior angles of a triangle = 180°
- Exterior angle = sum of the two non-adjacent interior angles
- Exterior angle + adjacent interior angle = 180° (a straight line)
Practice Problems
- In △ABC, ∠A=x°, ∠B=2x°, and ∠C=3x°. Find x.
- In △ABC, ∠A=40° and ∠B=80°. Find the exterior angle at vertex C.
Answer and Explanation
- Answer: x=30. x+2x+3x=180→6x=180.
- Answer: 120°. Exterior angle=40°+80°=120°.