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.

Algebra ->  Polygons -> 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.      Log On


   

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(52797) About Me  (Show Source):
Answer by greenestamps(13200) About Me  (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:

x%2B5x+=+180
6x+=+180
x+=+30

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.