For two vertical angles with measures m∠2=(5x+23)°

Question

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°.