Answer:
Explanation:
You want the measures of angles d° and e° in the given figure.
Assumptions
Usually, geometry problems tell you not to assume anything that isn't marked or stated regarding the figure. In order to answer this question, we need to assume ...
- ∆ACD is isosceles
- ∆ABE ~ ∆ACD
Isosceles triangle
The base angles in an isosceles triangle are congruent. That means each of them is the complement of half the vertex angle.
∠D = 90° -1/2∠A = 90° -8°/2 = 86°
The segments CD and BE are parallel, so angle E is the supplement of angle D:
∠E = 180° -86° = 94°
The angle measures are d° = 86° and e° = 94°.
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Additional comment
This is not a "word problem." All of the relations necessary for answering the question are shown in the diagram, not stated in words. (The question is necessarily written in words—for any problem.)
If b is a base angle and v is the vertex angle of an isosceles triangle, then the sum of angles is ...
b + b + v = 180°
2b = 180° -v . . . . . . subtract v
b = 90° -v/2 . . . . . . divide by 2
Effectively, the altitude of an isosceles triangle bisects the vertex angle and creates two congruent right triangles. The acute angles in that triangle are the original base angle and half the vertex angle. They are complementary.