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

Answer:

$m$∠$B=71$°

Step-by-step 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)

$\frac{19x}{19}=\frac{76}{19}$ (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!