Question

given parallelogram $jklm$ below, $mangle jnk = 63^{circ}$. if $mangle mnj=(-x + 9)^{circ}$, solve for $x$.

Explanation:

Step1: Note angle - sum property of a straight - line

The sum of angles on a straight - line is 180°. Since ∠JNK and ∠MNJ are adjacent angles on a straight - line, ∠JNK+∠MNJ = 180°.

Step2: Substitute the given angle measures

We know that m∠JNK = 63° and m∠MNJ=(-x + 9)°. So, 63+(-x + 9)=180.

Step3: Simplify the left - hand side of the equation

First, combine like terms: 63 - x+9=180, which simplifies to 72 - x=180.

Step4: Solve for x

Add x to both sides: 72=180 + x. Then subtract 180 from both sides: x=72 - 180=-108.

Answer:

x = - 108