Question

given
m∠lon is a straight angle.
m∠mon = 8x - 13°
m∠lom = 7x - 17°
find m∠mon:

Explanation:

Step1: Recall angle - addition postulate

Since $\angle LON$ is a straight angle, $m\angle LOM + m\angle MON=180^{\circ}$.

Step2: Substitute the given expressions

We have $(7x - 17)+(8x - 13)=180$.

Step3: Combine like - terms

$7x+8x-17 - 13 = 180$, which simplifies to $15x-30 = 180$.

Step4: Solve for $x$

Add 30 to both sides: $15x=180 + 30=210$. Then divide both sides by 15, so $x=\frac{210}{15}=14$.

Step5: Find $m\angle MON$

Substitute $x = 14$ into the expression for $m\angle MON$. $m\angle MON=8x-13$. So $m\angle MON=8\times14 - 13=112-13 = 99^{\circ}$.

Answer:

$99^{\circ}$