Answer:
75°
Explanation:
You want the measure of angle BDC in the given figure of an isosceles triangle.
Isosceles
The fact that triangle ABC is isosceles means the base angles at B and C are congruent. Their measure is ...
(180° -40°)/2 = 70°
Bisector
Segment BD bisects angle B, so each half will be half the measure of base angle B: 35°.
Exterior angle
Exterior angle BDC to triangle ABD will have a measure equal to the sum of the remote interior angles:
∠BDC = ∠DBA + ∠A
∠BDC = 35° +40° = 75°
The measure of ∠BDC is 75°.
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