In a diagram of a bridge, m∠1=87°

Question

. If ∠1
and ∠3
are vertical angles, and ∠2
and ∠3
are supplementary, what equation can you write to solve for the value of m∠2
? Let m∠2=x
.(1 point)
Responses

x+87°=90°
x plus 87 degrees equals 90 degrees

x+87°=180°
x plus 87 degrees equals 180 degrees

x=90°−87°
x equals 90 degrees minus 87 degrees

x=87°

Answer 1

To determine the relationship between the angles given, we can analyze the information provided:

1. Since ∠1 and ∠3 are vertical angles, they are equal. Therefore: \[ m∠3 = m∠1 = 87° \]

2. Since ∠2 and ∠3 are supplementary, they add up to 180°. So we can write the equation: \[ m∠2 + m∠3 = 180° \]

Substituting \( m∠3 = 87° \) into the equation gives: \[ m∠2 + 87° = 180° \]

If we let \( m∠2 = x \), the equation to solve for \( x \) becomes: \[ x + 87° = 180° \]

Thus, the equation you can write to solve for the value of \( m∠2 \) is: \[ \boxed{x + 87° = 180°} \]