Question

parallel ab, cd and np are shown with transversal ef. if m∠ehb = 48° and m∠jkc = 132°. what is the m∠pjk? select the previous answer is justified by: if two parallel lines are intersected by a transversal then

Explanation:

Step1: Identify angle - relationship

$\angle EHB$ and $\angle JKC$ are corresponding angles formed by parallel lines $\overleftrightarrow{AB}$, $\overleftrightarrow{CD}$ and transversal $\overleftrightarrow{EF}$.

Step2: Use angle - sum property

$\angle PJK$ and $\angle JKC$ are supplementary angles (linear - pair). The sum of the measures of two supplementary angles is $180^{\circ}$.

Step3: Calculate $\angle PJK$

Let $m\angle PJK=x$. We know that $m\angle JKC = 132^{\circ}$. Since $x + m\angle JKC=180^{\circ}$, then $x=180 - 132$.
$x = 48^{\circ}$

Answer:

$48^{\circ}$