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°=180°
x plus 87 degrees equals 180 degrees

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

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

x=87°

Answer 1

To solve for the value of \( m∠2 \) given that \( m∠1 = 87° \), we can use the properties of vertical angles and supplementary angles mentioned in the problem.

Since \( ∠1 \) and \( ∠3 \) are vertical angles, they are equal. Therefore,

\[ m∠3 = m∠1 = 87° \]

Next, since \( ∠2 \) and \( ∠3 \) are supplementary, we have:

\[ m∠2 + m∠3 = 180° \]

Substituting \( m∠3 = 87° \) into this equation gives us:

\[ m∠2 + 87° = 180° \]

If we let \( m∠2 = x \), we can write the equation as:

\[ x + 87° = 180° \]

Therefore, the correct equation to solve for \( m∠2 \) is:

x + 87° = 180°