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3 years ago

The complement of an angle is one-sixth the measure of the supplement of the angle. What is the measure of the complement angle?

Mathematics

2 answers:

DochEvi [55]3 years ago

8 0

Answer:

Option C.

The measure of the complement angle is $18\°$

Step-by-step explanation:

Let

x-----> the angle

we know that

The complement of an angle is equal to $(90-x)\°$

The supplement of an angle is equal to $(180-x)\°$

we have

The complement of an angle is one-sixth the measure of the supplement of the angle

$(90-x)\°=(1/6)(180-x)\°$

solve for x

$(540-6x)\°=(180-x)\°\\ (6x-x)=(540-180)\°\\ (5x)=(360)\°\\ x=72\°$

Find the measure of the complement angle

$(90-x)\° ----> (90-72)=18\°$

Jet001 [13]3 years ago

4 0

Answer:

Option C. 18

Step-by-step explanation:

<h2><em><u>Let x be the given angle. </u></em></h2><h2><em><u>1 </u></em></h2><h2><em><u>6 </u></em></h2><h2><em><u>(180 − x) = (90 − x) </u></em></h2><h2><em><u>30 − </u></em></h2><h2><em><u>1 </u></em></h2><h2><em><u>6 </u></em></h2><h2><em><u>x = 90 − x </u></em></h2><h2><em><u>5 </u></em></h2><h2><em><u>6 </u></em></h2><h2><em><u>x = 60 </u></em></h2><h2><em><u>x = 72° </u></em></h2><h2><em><u> </u></em></h2><h2><em><u>The supplement angle to 72° is 108°. </u></em></h2><h2><em><u>The complement angle to 72° is 18°.</u></em></h2>

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