Question

#12: m∠gkh = ____ °
(13x - 1)°
(9x + 3)°
your answer
#13: m∠mnq = ____ °
(2x - 1)°
(5x - 40)°

Explanation:

Step1: Identify angle - relationship for #12

Assume $\angle{GKH}$ and $\angle{JKG}$ are supplementary (a common situation if they form a linear - pair). So, $(13x - 1)+(9x + 3)=180$.

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Then, $m\angle{GKH}=(9x + 3)^{\circ}$. Substitute $x = \frac{89}{11}$ into the expression:

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Step2: Identify angle - relationship for #13

Assume $\angle{MNQ}$ and $\angle{PNR}$ are vertical angles (since they are opposite each other when two lines intersect). So, $2x-1 = 5x - 40$.

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Then, $m\angle{MNQ}=(2x - 1)^{\circ}$. Substitute $x = 13$ into the expression: $m\angle{MNQ}=2\times13-1=26 - 1=25^{\circ}$.

Answer:

#12: $\frac{834}{11}\approx75.82^{\circ}$
#13: $25^{\circ}$