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One of the exterior angles of a triangle is 100°. The interior opposite angle is 75°. Find the measure of all the angles of the triangle?
Given :
One of the exterior angles of a triangle is 100°.
The interior opposite angle is 75°.
To do:
We have to find all the angles of triangles.
Solution :
The sum of the angles in a linear pair is 180° and the sum of the angles in a triangle is 180°.
One of the exterior angles of a triangle is 100°.
This implies the adjacent interior angle is $180°-100°=80°$
Therefore,
The two angles of a triangle are 75° and 80°.
Let the third angle be x.
$75°+80°+x = 180°$
$155° + x = 180°$
$x = 180° -155°$
$x = 25°$
The measures of the angles of the given triangle are 25°, 75°, and 80°.
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