In △ABC, ∠B = 78º, AD is a bisector of ∠A meeting BC at D, and AE Ʇ BC at E. IF ∠DAE = 24º, then the measure of ∠ACB is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 30º
∠DAE = 24º, ∠B = 78º
In △ABE,
∠B + ∠E + ∠BAE = 180°
∠BAE = 180 - 78 - 90 = 12°.
∠BAD = 12 +24 = 36
AD is the angle bisector of ∠A so ∠BAD = ∠DAC = 36°
In △ABC,
∠B + ∠A + ∠C = 180
∠C = 180 - 78 - 72
∠C = 30°.