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

15.3°
15.3 degrees

53°
53 degrees

29°

Answer 1

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

\[
m∠2 = m∠4
\]

Substituting the given expressions:

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

Now, solve for \(x\):

1. Subtract \(3x\) from both sides:
\[
5x - 3x + 23 = 35
\]
This simplifies to:
\[
2x + 23 = 35
\]

2. Subtract \(23\) from both sides:
\[
2x = 12
\]

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

Now, substitute \(x\) back into either angle to find the measure. We can use \(m∠2\):

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

Now check \(m∠4\) to be sure:

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

Both angles measure \(53°\).

Thus, the measure of each angle is \( \boxed{53°} \).