the measures of an angle and its supplement gives the same quotient when divided by 7 and 13 respectively. Find the measure of the angle?


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David Shabazi Profile
David Shabazi answered

We have some angle, x°, and its supplement, 180°-x°.

When we divide these two by 7 and 13 respectively (so x°/7 and (180°-x°)/13), they'll both essentially equal to each other...

...So let's just do exactly that:

x/7 = (180-x)/13

13x/7 = 180-x (Multiplied both sides by 13)

13x = 1260-7x (Multiplied both sides by 7)

20x = 1260 (Added both sides by 7x)

x = 63° (Divided both sides by 20)

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