Question

he measures of the angles of a triangle are 50°, 35°, and 95°. What is the measure of the largest exterior angle of the triangle?

Answer 1

To find the largest exterior angle of a triangle, we first need to identify the largest interior angle. In this triangle, the angles are 50°, 35°, and 95°. The largest interior angle is 95°.

The exterior angle of a triangle is equal to 180° minus the measure of the interior angle. Therefore, the exterior angle corresponding to the largest interior angle (95°) is calculated as follows:

\[
\text{Exterior angle} = 180° - \text{Interior angle}
\]
\[
\text{Exterior angle} = 180° - 95° = 85°
\]

Next, we should also calculate the exterior angles corresponding to the other two angles to ensure we find the largest:

For the 50° angle:
\[
\text{Exterior angle} = 180° - 50° = 130°
\]

For the 35° angle:
\[
\text{Exterior angle} = 180° - 35° = 145°
\]

Among the exterior angles we calculated:
- Corresponding to 95°: 85°
- Corresponding to 50°: 130°
- Corresponding to 35°: 145°

The largest exterior angle is:
\[
\text{Largest exterior angle} = 145°
\]

Thus, the measure of the largest exterior angle of the triangle is **145°**.