Question

parallel lines p and q are intersected by transversal t. suppose m∠2 = 86°. what is the measure of ∠7? > type the answer in the space provided. use numbers instead of words. m∠7 =

Explanation:

Step1: Identify vertical - angle relationship

$\angle2$ and $\angle4$ are vertical angles, so $m\angle4 = m\angle2=86^{\circ}$ since vertical angles are congruent.

Step2: Identify corresponding - angle relationship

$\angle4$ and $\angle8$ are corresponding angles. Since $p\parallel q$, $m\angle4 = m\angle8 = 86^{\circ}$ (corresponding angles of parallel lines are congruent).

Step3: Identify supplementary - angle relationship

$\angle7$ and $\angle8$ are a linear - pair. So $m\angle7+m\angle8 = 180^{\circ}$.

Step4: Solve for $m\angle7$

$m\angle7=180 - m\angle8$. Substitute $m\angle8 = 86^{\circ}$, then $m\angle7=180 - 86=94^{\circ}$.

Answer:

$94$