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The third angle in an isosceles triangle is 10 more than 3 times as large as each of the two base angles. Find the measure of each angle.

Question

The third angle in an isosceles triangle is 10 more than 3 times as large as each of the two base angles. Find the measure of each angle.

The base angles are ??? degrees where the third angle is ??? degrees.

Please show a step by step explanation on how to do this

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Math
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2021-09-09T10:05:19+00:00
2021-09-09T10:05:19+00:00 1 Answer
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## Answers ( )

Answer: Each base angle is 34 degrees

The third angle is 112 degrees

Step-by-step explanation:

Let x represent the measure of each base angle of the isosceles triangle.

In an isosceles triangle, the base angles are equal.

The third angle in an isosceles triangle is 10 more than 3 times as large as each of the two base angles. This means that the measure of the third angle is

(3x + 10) degrees

The sum of the angles in a triangle is 180 degrees. Therefore

3x + 10 + x + x = 180

3x + x + x = 180 – 10

5x = 170

x = 170/5

x = 34

The measure of the third angle is

3x + 10 = 3 × 34 + 10

= 112