Question

in the figure shown, $t \parallel x$ and $k \parallel w$ and $m\angle 3 = 20$. 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 angles

Vertical angles are congruent. $\angle 3$ and $\angle 1$ are vertical angles, $\angle 3$ and $\angle 7$ are vertical angles, so $m\angle 1 = 20$, $m\angle 7 = 20$.

Step2: Identify alternate interior angles

Since $k \parallel w$, alternate interior angles are congruent. $\angle 3$ and $\angle 5$ are alternate interior angles, so $m\angle 5 = 20$.

Step3: Identify corresponding angles

Since $t \parallel x$ and $k \parallel w$, corresponding angles are congruent. $\angle 3$ corresponds to $\angle 14$, $\angle 9$, $\angle 11$, $\angle 16$, so $m\angle 14 = 20$, $m\angle 9 = 20$, $m\angle 11 = 20$, $m\angle 16 = 20$.

Step4: Confirm all congruent angles

Collect all angles with measure 20: $\angle 1, \angle 5, \angle 7, \angle 9, \angle 11, \angle 14, \angle 16$.

Answer:

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