One interior angle of a triangle is 98.5°, and the other two interior angles are congruent. What is the degree measure of one of the congruent angles?
a) 81.5°
b) 90°
c) 40.75°
d) 49.25°
The sum of the interior angles of a triangle is always 180°.
Let's denote the degree measure of one of the congruent angles as x. Since the other two angles are congruent, each of them also measures x°.
Therefore, we can set up the following equation:
98.5° + x° + x° = 180°
Combining like terms, we have:
98.5° + 2x° = 180°
Subtracting 98.5° from both sides, we get:
2x° = 81.5°
Dividing both sides by 2, we find:
x° = 40.75°
Therefore, the degree measure of one of the congruent angles is 40.75°.
The correct answer is therefore, c) 40.75°.