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Question

Suppose that CDE

 is isosceles with base CD

.

Suppose also that =m∠C+3x9°

 and =m∠D+2x24°

.Find the degree measure of each angle in the triangle.

Answer 1

I'm assuming you mean m∠C = 3x + 9 and m∠D = 2x + 24.

Since the triangle is isosceles, the two base angles are congruent so we can say m∠C = m∠D which means 3x + 9 = 2x + 24 [subtract 2x from each side to get:

x + 9 = 24 [subtract 9 from both sides to get:

x = 15.

So m∠C = 3(15) + 9 = 54° and m∠D also = 54°

Since there are 180° in a triangle m∠E = 180 - 54 - 54 = 72°