Question

find the value of x.
31°
74°
(2x - 5)°
x =

Explanation:

Step1: Set up angle - relationship equation

We know that the larger angle $\angle JNM=74^{\circ}$ and the smaller angle $\angle KNM = 31^{\circ}$, and $\angle JNK=(2x - 5)^{\circ}$. Since $\angle JNM=\angle JNK+\angle KNM$, we have the equation $74=(2x - 5)+31$.

Step2: Simplify the right - hand side of the equation

$(2x - 5)+31=2x+(31 - 5)=2x + 26$. So the equation becomes $74=2x + 26$.

Step3: Solve for x

Subtract 26 from both sides: $74-26=2x+26 - 26$, which gives $48 = 2x$. Then divide both sides by 2: $\frac{48}{2}=\frac{2x}{2}$, so $x = 24$.

Answer:

$24$