there is a pair of vertical angles whose measures are m<1 = 160 and m<2 = ( 3x - 75) what equation can you write to solve for x

Question

A. 3x - 75 + 106 = 90
B. 3x - 75 + 106 = 180
C. 3x - 75 - 106 = 180
D. 3x - 75 = 106

Answer 1

Vertical angles are equal in measure. Given that \( m\angle 1 = 160^\circ \) and \( m\angle 2 = 3x - 75 \), you can set up the equation:

\[ 160 = 3x - 75 \]

To solve for \( x \), you rearrange the equation:

1. Add 75 to both sides: \[ 160 + 75 = 3x \] \[ 235 = 3x \]

2. Divide by 3: \[ x = \frac{235}{3} \]

Thus, the appropriate equation you can write to solve for \( x \) is:

\[ 3x - 75 = 160 \]

However, since this doesn’t directly appear in the provided options, let’s look at your choices:

• A: \( 3x - 75 + 106 = 90 \)
• B: \( 3x - 75 + 106 = 180 \)
• C: \( 3x - 75 - 106 = 180 \)
• D: \( 3x - 75 = 106 \)

The equation we derived corresponds best with option D:

D: \( 3x - 75 = 106 \)

This can be manipulated to become equal to 160, thus making D the most suitable option to start from.