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

Question

2 years ago

12

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

1 answer:

Irina-Kira [14] · Answer 1 · 2023-09-03T16:27:52+03:00

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

<h3>What is the exterior angle theorem ?</h3>

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.

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