Question

For two vertical angles with measures m∠1 = (4x + 26)° and m∠3 = (3x + 32)°, what is the measure of each angle?

A. 6°

B. 24°

C. 50°

D. 64°

Answer 1

Vertical angles are opposite angles formed by the intersection of two lines. They are always congruent, which means they have the same measure.

Therefore, we can set up an equation to find the value of x:
m∠1 = m∠3
4x + 26 = 3x + 32
Subtract 3x from both sides: x + 26 = 32
Subtract 26 from both sides: x = 6

Now we can substitute the value of x back into the expressions for the angles to find their measures:
m∠1 = (4x + 26)°
m∠1 = (4*6 + 26)°
m∠1 = (24 + 26)°
m∠1 = 50°

m∠3 = (3x + 32)°
m∠3 = (3*6 + 32)°
m∠3 = (18 + 32)°
m∠3 = 50°

Therefore, the measure of each angle is 50°.

The answer is C. 50°.