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

29°
29 degrees

15.3°
15.3 degrees

6°
6 degrees

53°
53 degrees
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Answer 1

To find the measures of the vertical angles \( m∠2 \) and \( m∠4 \), we need to use the fact that vertical angles are equal. So, we set the expressions for the angles equal to each other:

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

Now, we will 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 the expressions for the angles to find their measures:

1. For \( m∠2 \):
\[
m∠2 = 5x + 23 = 5(6) + 23 = 30 + 23 = 53°
\]

2. For \( m∠4 \):
\[
m∠4 = 3x + 35 = 3(6) + 35 = 18 + 35 = 53°
\]

Therefore, both vertical angles measure \( 53° \).

The measure of each angle is **53°**.