Question

#12 m∠gkh =
your answer
this is a required question
#13 m∠mnq =

Explanation:

Step1: Assume the two angles are supplementary

If the two angles $\angle{JGK}=(13x - 1)^{\circ}$ and $\angle{GKH}=(9x + 3)^{\circ}$ are supplementary (form a straight - line), then their sum is $180^{\circ}$. So, $(13x-1)+(9x + 3)=180$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $13x+9x-1 + 3=180$, which gives $22x+2 = 180$.

Step3: Solve for x

Subtract 2 from both sides: $22x=180 - 2=178$. Then $x=\frac{178}{22}=\frac{89}{11}\approx8.09$.

Step4: Find the measure of $\angle{GKH}$

Substitute $x$ into the expression for $\angle{GKH}$: $m\angle{GKH}=(9x + 3)^{\circ}$. Plugging in $x=\frac{89}{11}$, we have $9\times\frac{89}{11}+3=\frac{801}{11}+3=\frac{801+33}{11}=\frac{834}{11}\approx75.82^{\circ}$.

Answer:

$\frac{834}{11}^{\circ}$ (or approximately $75.82^{\circ}$)