Question

Use your knowledge of parallel lines and same-side interior angles to solve this problem. In this parallelogram, the measure of ∠B exceeds the measure of ∠A by 30°. What is the measure of ∠C?

a) 60°
b) 75°
c) 90°
d) 120°

Answer 1

The measure of angle C in the parallelogram is 75°, determined by using properties of parallelograms and the fact that angle B exceeds angle A by 30°.

Step-by-step explanation:

To solve the problem using knowledge of parallel lines and same-side interior angles, we must understand that in a parallelogram, opposite angles are equal, and the sum of any two adjacent angles is 180°. Since the measure of ∠B exceeds the measure of ∠A by 30°, and knowing that ∠A and ∠C are opposite angles in a parallelogram, they must be equal. Therefore, if ∠A is x°, then ∠B would be x° + 30°. Additionally, because the sum of angles ∠A and ∠B must equal 180°, we can set up the equation x + (x + 30°) = 180°. Solving for x gives us x = 75°, which means ∠A is 75°, and ∠C being equal to ∠A is also 75°. Therefore, the measure of ∠C is 75° and the correct answer is b) 75°.