Question

For two vertical angles with measures m<2 = ( 5x + 23 ) and m<4 = ( 3x + 35 ). what is the measure of each angle?

29

15.3

53

6

Answer 1

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

\[
m\angle 2 = m\angle 4
\]

Substituting the given expressions:

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

Now, let's 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:

\[
2x = 35 - 23
\]

This simplifies to:

\[
2x = 12
\]

3. Divide both sides by 2:

\[
x = 6
\]

Now that we have \(x\), we can find the measures of the angles:

1. Substitute \(x\) back into the expression for \(m\angle 2\):

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

2. Substitute \(x\) back into the expression for \(m\angle 4\):

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

Thus, the measure of each angle is:

\[
\boxed{53}
\]