SOLUTION: an interior angle of an isosceles triangle is the measure of the adjacent exterior angle multiplied by 5. determine the measure of each interior angle of the triangle.

Question 1150932: an interior angle of an isosceles triangle is the measure of the adjacent exterior angle multiplied by 5. determine the measure of each interior angle of the triangle.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52800) (Show Source): You can put this solution on YOUR website!

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

x = exterior angle
5x = interior angle

The sum of the interior and exterior angle is 180 degrees:

The exterior angle is x=30 degrees.
The interior angle is 5x=150 degrees.

Since the triangle is isosceles and the sum of the three interior angles of the triangle is 180 degrees, the 150-degree interior angle can't be one of the congruent base angles; it is the vertex angle.

And then, since the two base angles are equal and the vertex angle is 150 degrees, each of the two base angles is 15 degrees.

ANSWER: The angles of the triangle are 150, 15, and 15 degrees.

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