Question

∠A and \angle B∠B are complementary angles. If m\angle A=(2x+10)^{\circ}∠A=(2x+10) ∘ and m\angle B=(3x+15)^{\circ}∠B=(3x+15) ∘ , then find the measure of \angle B∠B.

Answer 1

Answer:

$54^\circ$

Step-by-step explanation:

Given :

$m\angle A=(2x+10)^{\circ}$

$m\angle B=(3x+15)^{\circ}$

And angles $\angle A$ and $\angle B$ are complementary angles.

To find:

The measure of $\angle B$.

Solution:

First of all, let us learn about complementary angles.

Complementary angles are the angles whose sum is equal to $90^\circ$.

And we are given that angles $\angle A$ and $\angle B$ are complementary angles.

Therefore $\angle A$ + $\angle B$ = $90^\circ$

$\Rightarrow 2x+10+3x+15=90\\\Rightarrow 5x+25=90\\\Rightarrow 5x=65\\\Rightarrow x =13$

Putting the value in $\angle B$.

$m\angle B=(3\times 13+15)^{\circ} = 54^\circ$

Therefore, the answer is $\bold{\angle B = 54^\circ}$