Question

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

Answer 1

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.