Question

in the figure shown, (tparallel x) and (kparallel w) and (mangle3 = 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 pairs

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

Step2: Use corresponding - angle property for parallel lines

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

Step3: Use alternate - interior and alternate - exterior angle properties

$\angle3$ and $\angle7$ are alternate - exterior angles (because $k\parallel w$ and $t\parallel x$), so $m\angle7 = 20$. $\angle3$ and $\angle9$ are alternate - interior angles (because $k\parallel w$ and $t\parallel x$), so $m\angle9 = 20$. $\angle3$ and $\angle11$ are corresponding angles for the parallel lines $t$ and $x$ with transversal $w$, so $m\angle11 = 20$. $\angle3$ and $\angle14$ are vertical angles to corresponding angles, so $m\angle14 = 20$. $\angle3$ and $\angle16$ are vertical angles to alternate - exterior angles, so $m\angle16 = 20$.

Answer:

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