Two angles are supplementary. If the ratio of the measure of the smaller angle to that of the larger angle is 5: 7, what is the measure of the smaller angle?

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24-03-2018
Mathematics

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Two angles are supplementary. If the ratio of the measure of the smaller angle to that of the larger angle is 5: 7, what is the measure of the smaller angle?

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cedarwood79 cedarwood79 · Answer 1 · 2018-03-24T02:15:14+01:00

Hello! A supplementary angle measures 180 degrees. The ratio is 5:7. To solve for the angles, we will set up and solve an equation. 5x + 7x is 12x. 12x = 180 is an equation we can use. Let's solve for the value of x. 12x/12 cancels out. 180/12 is 15. Let's plug in this value and see what happens. 15 * 5 is 75. 7 * 15 is 105. 105 + 75 = 180. 75 : 105 is the ratio and when you divide each side by 15, you get 5 : 7. There. The measurement of the smaller angle is 75 degrees.