Question

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

Explanation:

Step1: Identify angle - relationship

The large angle $\angle JNM$ is composed of two smaller angles $\angle JNK$ and $\angle KNM$. So, $\angle JNK=\angle JNM+\angle KNM$.

Step2: Substitute angle - values

We know that $\angle JNK = 74^{\circ}$, $\angle KNM=31^{\circ}$, and $\angle JNM=(2x - 5)^{\circ}$. Then $74^{\circ}=(2x - 5)^{\circ}+31^{\circ}$.

Step3: Solve the equation for x

First, simplify the right - hand side of the equation: $(2x - 5)+31=2x+26$. So the equation becomes $74 = 2x+26$.
Subtract 26 from both sides: $74 - 26=2x$, which gives $48 = 2x$.
Divide both sides by 2: $x=\frac{48}{2}=24$.

Answer:

$24$