Question

1 select the correct answer. in the figure, $overline{bc}$ and $overline{ad}$ are line - segments. what is the sum of $x$ and $y$?

Explanation:

Step1: Find vertical - angle

The vertical - angle to the $64^{\circ}$ angle is also $64^{\circ}$.

Step2: Calculate $x$ in $\triangle ABO$

In $\triangle ABO$, using the angle - sum property of a triangle ($180^{\circ}$), $x = 180^{\circ}-62^{\circ}-64^{\circ}=54^{\circ}$.

Step3: Calculate $y$ in $\triangle DOC$

In $\triangle DOC$, using the angle - sum property of a triangle, $y = 180^{\circ}-54^{\circ}-64^{\circ}=62^{\circ}$.

Step4: Calculate $x + y$

$x + y=54^{\circ}+62^{\circ}=116^{\circ}$.

Answer:

B. $116^{\circ}$