Question

in the figure shown, t || x and k || w and m∠3 = 20. choose the list which includes all of the other angles that measure 20.
a. 1
b. 7, 9, 14
c. 1, 14, 16
d. 1, 5, 7, 9, 11, 14, 16

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle3$ and $\angle1$ are vertical angles, so $m\angle1 = 20$.

Step2: Identify corresponding - angle relationship

Since $t\parallel x$ and $k\parallel w$, $\angle3$ and $\angle5$ are corresponding angles, so $m\angle5 = 20$.

Step3: Identify alternate - interior and alternate - exterior angle relationships

$\angle3$ and $\angle7$ are alternate - interior angles, so $m\angle7 = 20$. $\angle3$ and $\angle9$ are alternate - exterior angles, so $m\angle9 = 20$. $\angle3$ and $\angle11$ are also alternate - exterior angles, so $m\angle11 = 20$. $\angle3$ and $\angle14$ are alternate - interior angles, so $m\angle14 = 20$. $\angle3$ and $\angle16$ are corresponding angles, so $m\angle16 = 20$.

Answer:

D. 1, 5, 7, 9, 11, 14, 16