If you remember the properties of complementary and supplementary angles, this will definitely come in handy for the Praxis Core exam. If you don’t, check out the following tip and practice questions to refresh your memory.
When two adjacent angles add up to 90 degrees (forming a right angle), they are complementary. When two adjacent angles add up to 180 degrees (forming a straight angle, or linear pair), they are supplementary.
Both of the following practice questions contain diagrams. In the first one, you’re shown one angle in a linear pair, and you have to calculate the missing supplementary angle. In the second problem, you’re shown one angle in a right angle, and you have to find its missing complementary angle.Practice questions
Use the following diagram to answer the first question.
- What is the measure of angle ABD?
A. 121 degrees B. 31 degrees C. 59 degrees D. 61 degrees E. 149 degrees
- What is the value of x in the following diagram?
A. 143 B. 53 C. 233 D. 37 E. 63
Answers and explanations
- The correct answer is Choice (C). Angle ABD and angle DBC form a linear pair, so they're supplementary. Therefore, the sum of their measures is 180 degrees. The measure that must be added to 121 degrees is 59 degrees because 180 – 121 = 59. Therefore, the measure of angle ABD is 59 degrees.
- The correct answer is Choice (B).
You can work a problem like this by setting up an algebraic equation. Here, the sum of x and 37 must be 90 because the two angles are complementary. They form a right angle together, so the sum of their measures is 90 degrees.
