Question

∠A and ∠ B ∠B are vertical angles. If m ∠ A = ( 2 x + 7 ) ∘ ∠A=(2x+7) ∘ and m ∠ B = ( 5 x + 16 ) ∘ ∠B=(5x+16) ∘ , then find the measure of ∠ B ∠B.

Answer 1

Vertical angles are congruent angles formed by intersecting lines. To find the measure of ∠B, we set up an equation and solve for x. Substituting the value of x, we find that the measure of ∠B is 1°.

Step-by-step explanation:

Vertical angles are formed when two lines intersect. They are congruent, meaning they have the same measure.

Based on the given information, ∠A and ∠B are vertical angles. We are given that m ∠A = (2x + 7)° and m ∠B = (5x + 16)°.

Since ∠A and ∠B are vertical angles, they have the same measure. So we can set up an equation: (2x + 7) = (5x + 16).

Now, we solve the equation:

2x + 7 = 5x + 16

7 - 16 = 5x - 2x

-9 = 3x

x = -3

Substituting x = -3, we can find the measure of ∠B:

m ∠B = (5x + 16)° = (5(-3) + 16)° = 1°

Therefore, the measure of ∠B is 1°.