Select the correct answer.
Two exterior angles of a triangle measure 135° and 100°. What are the measures of the interior angles of the triangle?
A.
45°, 65°, 80°
B.
45°, 65°, 70°
C.
45°, 55°, 80°
D.
55°, 75°, 50°
E.
80°, 50°, 50°
C. 45°, 55°, 80°
To find the measures of the interior angles of a triangle, we can use the fact that the sum of the interior angles of a triangle is always 180°.
Let's calculate the measure of the third interior angle by subtracting the two given exterior angles from 180°:
Third interior angle = 180° - (135° + 100°)
Third interior angle = 180° - 235°
Third interior angle = -55°
Since the third interior angle is negative, this does not make sense in the context of a triangle. Therefore, the given angles do not form a valid triangle.
There is no correct answer from the options provided.