To solve this problem, let's first understand the relationship between exterior and interior angles in a triangle. The exterior angle is supplementary to its corresponding interior angle. This means that the sum of an exterior angle and its corresponding interior angle is 180°.
Step 1: Identify the third exterior angle.
Given:
- Exterior angle 1 = 135°
- Exterior angle 2 = 100°
For any triangle, the sum of all exterior angles is always 360°. Thus:
[tex]\[ 135° + 100° + \text{Exterior angle 3} = 360° \][/tex]
Solving for Exterior angle 3:
[tex]\[
\text{Exterior angle 3} = 360° - (135° + 100°)
\][/tex]
[tex]\[
\text{Exterior angle 3} = 360° - 235°
\][/tex]
[tex]\[
\text{Exterior angle 3} = 125°
\][/tex]
Step 2: Calculate the interior angles.
To find the interior angles, we use the fact that each interior angle is supplementary to its corresponding exterior angle:
- Interior angle 1 = 180° - 135° = 45°
- Interior angle 2 = 180° - 100° = 80°
- Interior angle 3 = 180° - 125° = 55°
So, the measures of the interior angles are:
45°, 80°, 55°
Step 3: Compare these measures with the given choices:
A. 45°, 65°, 80° (not a match)
B. 45°, 65°, 70° (not a match)
C. 45°, 55°, 80° (match)
D. 55°, 75°, 50° (not a match)
E. 80°, 50°, 50° (not a match)
Therefore, the correct choice is:
C. 45°, 55°, 80°
