Question

3.4.6 check your understanding
in the figure shown $overline{yb}paralleloverline{cd},m\angle krm = 41^{circ}$ and $m\angle dwk = 109^{circ}$.
determine the measures of $\angle ykw$ and $\angle cmr$.
m\angle ykw =
\\(^{circ})
m\angle cmr =
\\(^{circ})

Explanation:

Step1: Identify vertical - angles

Vertical angles are equal. $\angle YKW$ and $\angle DWF$ are vertical angles. Given $m\angle DWK = 109^{\circ}$, and since $\angle DWK+\angle DWF = 180^{\circ}$ (linear - pair of angles), then $m\angle DWF=180 - 109=71^{\circ}$. So, $m\angle YKW = 71^{\circ}$.

Step2: Use the property of parallel lines

Since $\overline{YB}\parallel\overline{CD}$, $\angle KRM$ and $\angle CMR$ are alternate - interior angles. Alternate - interior angles formed by two parallel lines and a transversal are equal. Given $m\angle KRM = 41^{\circ}$, so $m\angle CMR = 41^{\circ}$.

Answer:

$m\angle YKW = 71$
$m\angle CMR = 41$