In ΔABC, AD is perpendicular to BC and AE is the bisector of ∠ABC = 58º and ∠ACB = 34º, then find the measure of ∠DAE.
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Correct answer: A
Explanation
The correct answer is option 1 i.e. 12º
angle(A) = 180 - angle(B) - angle(C)
⇒ angle(A) = 180 - 58 - 34 = 180 - 92 = 88°
Therefore, angle(BAE) = 88/2 = 44°
In triangle(BAE) ,
angle(BEA) = 180 - angle(BAE) - angle(B)
⇒ angle(BEA) = 180 - 44 - 58 = 180 - 102 = 78°
In triangle(ADE),
angle(DAE) = 180 - angle(BEA) - angle(ADE)
⇒ angle(DAE) = 180 - 78 - 90 = 180 - 168 = 12°