document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #772508 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "x = exterior angle
\n" ); document.write( "5x = interior angle

\n" ); document.write( "The sum of the interior and exterior angle is 180 degrees:

\n" ); document.write( " $\"x%2B5x+=+180\"$
\n" ); document.write( " $\"6x+=+180\"$
\n" ); document.write( " $\"x+=+30\"$

\n" ); document.write( "The exterior angle is x=30 degrees.
\n" ); document.write( "The interior angle is 5x=150 degrees.

\n" ); document.write( "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.

\n" ); document.write( "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.

\n" ); document.write( "ANSWER: The angles of the triangle are 150, 15, and 15 degrees.

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