SOLUTION: Two supplementary angles are in the ratio of 11:7. Find the measure of the smaller angle.

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Question 230562: Two supplementary angles are in the ratio of 11:7. Find the measure of the smaller angle.
Answer by drj(1380) About Me  (Show Source):
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Two supplementary angles are in the ratio of 11:7. Find the measure of the smaller angle.

Step 1. Supplementary angles means two angles add up to 180 degrees.

Step 2. Let x be one angle.

Step 3. Let 180-x be its supplementary angle.

Step 4. 11%2F7=x%2F%28180-x%29 since the ratio of two supplementary angles is 11:7.

Step 5. Solving 11%2F7=x%2F%28180-x%29 yields the following steps

Multiply 7(180-x) to both sides of the equation



%28180-x%29%2A11=7x

1980-11x=7x

Add 11x to both sides of the equation

1980-11x%2B11x=7x%2B11

1980=18x

Divide by 18 to both sides of the equation

1980%2F18=18x%2F18

x=110 and 180-x=70. Also note the ratio of 110%2F70=11%2F7

Step 6. ANSWER: The smaller angle is 70 degrees.

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J