PSAT Math Multiple-Choice Question 76: Answer and Explanation

Question: 76

In the figure above, BC || AD. What is the measure of ∠ACD?

• A. 35
• B. 40
• C. 50
• D. 55

Correct Answer: C

Explanation:

C

The question asks for the value of an angle on a figure. Use the geometry basic approach. Start by labeling the figure with the given information. Mark BC and AD as parallel. It may not be immediately obvious how to get the value of ∠ACD, so see what else can be determined. Any time a line crosses two parallel lines, all of the small angles have the same measure and all of the big angles have the same measure. The big and small angles are supplementary angles: the sum of the measure of any big angle plus any small angle equals 180°. In this figure, ∠BCD and ∠ADC are supplementary big and small angles. Because ∠ADC has a measure given of 95°, subtract 95 from 180 to see that ∠BCD must have a measure of 85°. Subtract 35 from 85 to see that ∠ACD must have a measure of 50°. The correct answer is (C).