Answer:
A. 63°
Explanation:
You want to know the base angle in the isosceles triangle in the given figure.
Angle sum
Angle ABC is the sum of its parts:
∠ABC = ∠ABD +∠DBC
The figure shows ∆DBC is equilateral, so ∠DBC = 60°. This lets us solve for the measure of angle ABD:
114° = ∠ABD +60°
54° = ∠ABD
Base angle
∆ABD is isosceles, so the two base angles are congruent. The sum of angles in the triangle is 180°, so we have ...
∠ABD +∠BAD +∠BDA = 180°
54° +2(∠BAD) = 180° . . . . . . . ∠BAD =∠BDA
∠BAD = 90° -27° . . . . . . divide by 2, subtract 27°
∠BAD = 63°