The size of an exterior angle of a triangle is the supplement of smaller of two opposite interior angles If the greater of the opposite interior angles exceeds the smaller by 30 degrees , find the measure of the interior angles of the triangle.

The two interior angles of the triangle is 75 and 105 degree.

What is the exterior angle theorem ?

According to the exterior angle theorem , The size of an exterior angle of a triangle is the sum of of smaller of two opposite interior angles.

It is given that

Let the measure of the two interior angle be x and y

then

The size of an exterior angle of a triangle is the supplement of smaller of two opposite interior angles

x+ y = 180

the greater of the opposite interior angles exceeds the smaller by 30 degrees , find the measure of the interior angles of the triangle.

x = y+30

By substitution method

y+30+y = 180

2y +30 = 180

2y = 150

y = 75 degree and x = 105 degree.

Therefore the two interior angles of the triangle is 75 and 105 degree.

interiorangles of thetriangleis 75 and 105 degree.## What is the exterior angle theorem ?

exterior angleof a triangle is the supplement of smaller of two opposite interior anglesinterior anglesexceeds the smaller by 30 degrees , find the measure of theinterior anglesof thetriangle.substitutionmethodinterior anglesof thetriangleis 75 and 105 degree.exterior angletheorem