Question

one of the exterior angles of an isosceles triangle is 115 degrees. find the angles of this triangle.
The measures of the angles of the triangles are _,_,_ or _,_,_

Answer 1

In an isosceles triangle, there are two equal angles, and an exterior angle is equal to the sum of the two non-adjacent interior angles.

Given that one of the exterior angles is 115 degrees, we can set up the equation for the interior angles. Let's denote the equal interior angles of the isosceles triangle as \( x \). Then, according to the exterior angle theorem:

\[
115 = x + x = 2x
\]

Now, we can solve for \( x \):

\[
2x = 115 \\
x = \frac{115}{2} \\
x = 57.5 \text{ degrees}
\]

Thus, the two equal angles in the isosceles triangle are 57.5 degrees each.

To find the third angle, we use the fact that the sum of all interior angles in a triangle is always 180 degrees:

\[
\text{Third angle} = 180 - (57.5 + 57.5) = 180 - 115 = 65 \text{ degrees}
\]

Therefore, the measures of the angles of the isosceles triangle are:

\[ 57.5, 57.5, 65 \text{ degrees} \]

Or, as requested, we can express it as:

**The measures of the angles of the triangles are 57.5, 57.5, 65 or 57.5, 57.5, 65.**