Question

An angle's measure is 3 times the measure of its complement. Find the measures of DP and the adjacent angles.

a) DP = 30 degrees, adjacent angles = 60 degrees
b) DP = 20 degrees, adjacent angles = 70 degrees
c) DP = 45 degrees, adjacent angles = 135 degrees
d) DP = 15 degrees, adjacent angles = 75 degrees

Answer 1

The measure of DP is 67.5 degrees and the measure of its complement is 22.5 degrees. The adjacent angles measure 67.5 degrees and 22.5 degrees, respectively.

Step-by-step explanation:

Let's assign the measure of the angle DP to be 'x' degrees. According to the given information, the measure of the complement of DP is (90 - x) degrees. We are told that the measure of DP is 3 times the measure of its complement, so we can write the equation: x = 3(90 - x).

Simplifying the equation, we have: x = 270 - 3x. Combining like terms, we get: 4x = 270. Dividing both sides by 4, we find: x = 67.5.

Therefore, DP measures 67.5 degrees and its complement measures (90 - 67.5) = 22.5 degrees. The adjacent angles are the angles that are next to DP and its complement, so they measure 67.5 degrees and 22.5 degrees, respectively.