In △ABC, M and N are the points on side BC such that AM Ʇ BC, AN is the bisector of ∠A, and M lies between B and N. If ∠B = 68º, and ∠C = 26º, then the measure of ∠MAN is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 21º.
In △ABC,
∠A + ∠B + ∠C = 180°
∠A = 180 - 68 - 26 = 86°
∠BAN = ∠NAC = 1/2 of 86 = 43°
In △ABM,
∠ABM + ∠BAM + ∠AMB = 180
68° + ∠BAM + 90 = 180°.
∠BAM = 22.
∠MAN = 43 - 22 = 21°.