In ABC, if CB AC≅ , m∠A = 3x + 18, m∠B = 7x – 58, and m∠C = 2x – 8, find x and the measure of each angle.

Mathematics

1 answer:

lesya692 [45]2 years ago

6 0

9514 1404 393

Answer:

x = 19

A = 30°

B = C = 75°

Step-by-step explanation:

In an isosceles triangle, the angles opposite the congruent sides have the same measures.

A = B

3x +18 = 7x -58

76 = 4x . . . . . . . . add 58-4x

19 = x . . . . . . . . . divide by 4

Then the equal angles measure ...

A = B = 3(19) +18 = 75

C = 2(19) -8 = 30

Angles A, B, C measure 75°, 75°, 30°, respectively.

_____

<em>Alternate solution</em>

The sum of angles in a triangle is 180°, so you could write ...

(3x +18) +(7x -58) +(2x -8) = 180

12x = 228 . . . . . add 48

x = 19 . . . . . divide by 12

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