For two vertical angles with measures m∠2=(5x+23)° and m∠4=(3x+35)° , what is the measure of each angle?(1 point)

Question

Responses

15.3°
15.3 degrees      

53°
53 degrees

6°
6 degrees    

29°

Pls be right

Answer 1

To find the measures of the vertical angles, we can set the two expressions equal to each other, since vertical angles are congruent. So, we have:

\[ m∠2 = m∠4 \] \[ 5x + 23 = 3x + 35 \]

Now, we can solve for \(x\):

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

2. This simplifies to: \[ 2x + 23 = 35 \]

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

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

Now that we have the value of \(x\), we can substitute it back into either angle measure to find the measures of \(m∠2\) and \(m∠4\).

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

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

Thus, the measures of the angles are:

• \(m∠2 = 53°\)
• \(m∠4 = 53°\)

Therefore, the correct answer is \(53\) degrees.