Question

angle A and B are complementary. Angle A is (2x+11) and angle B=(17x+3). what is the Measure of angle B?

Answer 1

`m`∠
`B=71`°

Explanation:

Complementary angles are a pair of angles whose measures have a sum of
`90`°. Therefore,
`m`∠
`A+m`∠
`B=90`°. We are given that
`m`∠
`A=2x+11` and
`m`∠
`B=17x+3`. Substituting these values into our equation gives us:

`2x+11+17x+3=90`

Solving for
`x`, we get:

`2x+11+17x+3=90`

`19x+14=90` (Simplify LHS)

`19x+14-14=90-14` (Subtract
`14` from both sides of the equation to isolate
`x`)

`19x=76` (Simplify)

`(19x)/(19)=(76)/(19)` (Divide both sides of the equation by
`19` to get rid of
`x`'s coefficient)

`x=4` (Simplify)

Therefore,
`m`∠
`B=17x+3=17(4)+3=68+3=71`°. Hope this helps!