Question

For two vertical angles with measures m∠2=(5x+23)°
and m∠4=(3x+35)°
, what is the measure of each angle?(1 point)
Responses

6°
6 degrees

53°
53 degrees

15.3°
15.3 degrees

29°
29 degrees

Answer 1

Vertical angles are congruent, which means that their measures are equal.

Given:
- \( m\angle 2 = (5x + 23)^\circ \)
- \( m\angle 4 = (3x + 35)^\circ \)

Since the angles are equal:
\[
5x + 23 = 3x + 35
\]

Now, let's solve for \( x \):
1. Subtract \( 3x \) from both sides:
\[
5x - 3x + 23 = 35
\]
\[
2x + 23 = 35
\]

2. Subtract 23 from both sides:
\[
2x = 35 - 23
\]
\[
2x = 12
\]

3. Divide by 2:
\[
x = 6
\]

Now, substitute \( x \) back into either angle expression to find the measures of the angles:

Using \( m\angle 2 \):
\[
m\angle 2 = 5(6) + 23 = 30 + 23 = 53^\circ
\]

Using \( m\angle 4 \):
\[
m\angle 4 = 3(6) + 35 = 18 + 35 = 53^\circ
\]

Thus, both angles measure \( 53^\circ \).

Therefore, the measure of each angle is \( 53^\circ \).