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Two exterior angles of a triangle measure 135° and 100°. What are the measures of the interior angles of the triangle?
OA. 45°, 65°, 80°
O B.
45°, 65°, 70°
â—‹ C.
45°, 55°, 80°
O D.
55°, 75°, 50°
OE
80°, 50°, 50°
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Answer :

GinnyAnswer
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°

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