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?

Question

a) 81.5°

b) 90°

c) 40.75°

d) 49.25°

Answer 1

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°.