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. If x /2 − 9° and x /3 + 14° are complement to each other, find the value of x

User Danielv
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1 Answer

4 votes

Answer:

102

Explanation:

complementary angles are two angles that sum to 90°.

here we have two different angles, the first thing to do is sum them:


( (x)/(2) - 9) + ( (x)/(3) + 14)


\to( (x)/(2) + (x)/(3) ) - 9 + 14

we will convert the fractions to ones that have a common denominator of 6.


( (x)/(2) + (x)/(3) ) = ( (3x)/(6) + (2x)/(6) )

next, we just sum them and get


(5x)/(6)

so, we have


(5x)/(6) + 5 = 90

subtract 5 from both sides.


(5x)/(6) = 85

next, divide both sides by 5/6, or multiply both sides by 6/5.


x = 85 * (6)/(5) = 17 * 6 = 102

so, we have x as 102.

User Aurelije
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