Question

#12: x =
your answer
this is a required question
#12: m∠mnq =
your answer
#12: m∠qnp =

Explanation:

Step1: Assume $\angle MNQ$ and $\angle QNP$ are adjacent - angles and $\angle MNP$ is a whole - angle. If $\angle MNP$ is a straight - angle ($180^{\circ}$) or we assume some angle - addition postulate relationship. Let's assume $\angle MNQ+\angle QNP$ forms a certain angle relationship. Here, we assume $\angle MNQ$ and $\angle QNP$ are non - overlapping and their sum is related to a known angle property. If we assume $\angle MNQ$ and $\angle QNP$ are such that $4x - 18+x + 7$ is related to a known angle value. For simplicity, if we assume they are adjacent angles and their sum is a whole angle (say a straight angle $180^{\circ}$, although it's not given explicitly, a common case in angle problems), we set up the equation:

$4x-18+x + 7=180$

Step2: Combine like terms

$(4x+x)+(-18 + 7)=180$
$5x-11 = 180$

Step3: Add 11 to both sides of the equation

$5x-11+11=180 + 11$
$5x=191$
$x=\frac{191}{5}=38.2$

Step4: Find $m\angle MNQ$

Substitute $x = 38.2$ into the expression for $\angle MNQ$:
$m\angle MNQ=4x-18=4\times38.2-18=152.8 - 18=134.8^{\circ}$

Step5: Find $m\angle QNP$

Substitute $x = 38.2$ into the expression for $\angle QNP$:
$m\angle QNP=x + 7=38.2+7=45.2^{\circ}$

Answer:

$x = 38.2$
$m\angle MNQ=134.8^{\circ}$
$m\angle QNP=45.2^{\circ}$