Ratio of an angle

Question

the ratio of the measurement of an angle to its supplement is 2:3. find the measurement of the angle and its supplement

Answer 1

Supplementary angles have a sum of 180°.

For this problem, the ratio 2:3 is comparing one of the angles to the other. This is the same as comparing one of the angles to the total of the two, which is 5. This can be used to create two part-to-whole ratios and use them to find the measures of the angles themselves.

2 (smaller angle) = x° (smaller angle)

5 total 180° total

Since 5 times 36 is 180, you can multiply the numerator and denominator by 36 to determine the smaller of the two angles:

2 • 36 = 72°

5 • 36 180°

The smaller angle is 72.° The larger angle will be 180-72 or 108 °

To check, 72:108 is equivalent to 2:3