Question

In a triangle ABC, angle bisector of ∠B and ∠A intersect at O. ∠C is 82°. What is the measure of ∠BOA?

• A. 121°
• B. 131°
• C. 151°
• D. 90°

Answer 1

Answer:

B. 131°

Solution:

Given:

The measure of ∠C = 82° 

Concept used:

The sum of all the angles of the triangle is 180° 

Calculation:

∠A + ∠B + ∠C = 180° 

Dividing by 2

∠A/2 + ∠B/2 + ∠C/2 = 180°/2

⇒ ∠A/2 + ∠B/2 = 90° - 82°/2

⇒ ∠A/2 + ∠B/2 = 49° 

In ΔAOB 

∠A/2 + ∠B/2 + ∠BOA = 180° 

⇒ ∠BOA = 180° - 49° 

⇒ ∠BOA = 131° 

Shortcut Trick

Concept:

The (interior) bisector of an angle, also called the internal angle bisector, is the line or line segment that divides the angle into two equal parts.

Calculation:

Measure of ∠BOA = (90 + ∠C/2) = (90° + 41°) = 131°