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

53°
53 degrees

29°
29 degrees

6°
6 degrees

15.3°

Answer 1

Vertical angles are equal, so we can set the two expressions equal to each other:

\[
5x + 23 = 3x + 35
\]

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:
\[
2x = 12
\]

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

Now that we have \( x \), we can substitute it back into either angle measure to find the measures of the angles. We'll use the measure of \( m∠2 \):

\[
m∠2 = 5(6) + 23
\]
\[
m∠2 = 30 + 23
\]
\[
m∠2 = 53°
\]

Now we'll check \( m∠4 \) to ensure it's the same:

\[
m∠4 = 3(6) + 35
\]
\[
m∠4 = 18 + 35
\]
\[
m∠4 = 53°
\]

Thus, the measures of both angles are \( 53° \).

The answer is **53°**.