Question

find the measure of ∠jpn.
m∠jpn = □°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle KOL$ and $\angle MPN$ are vertical angles. So, $105 - x=2x + 84$.

Step2: Solve the equation for $x$

Add $x$ to both sides: $105=2x + 84+x$, which simplifies to $105 = 3x+84$. Then subtract 84 from both sides: $105 - 84=3x$, so $21 = 3x$. Divide both sides by 3: $x = 7$.

Step3: Find the measure of $\angle JPN$

$\angle JPN$ and $\angle MPN$ are supplementary (linear - pair of angles), so $\angle JPN=180-(2x + 84)$. Substitute $x = 7$ into the expression: $2x+84=2\times7 + 84=14 + 84 = 98$. Then $\angle JPN=180 - 98=82^{\circ}$.

Answer:

$82$