Question

find the values of x and y. 11. 12. 13.

Explanation:

Step1: Use vertical - angle property for 11

Vertical angles are equal. So for the first figure (11), $x = 81$ since the angle opposite to the $81^{\circ}$ angle and $x$ are vertical angles. And $y$ is also $81^{\circ}$ as it is vertical to the $81^{\circ}$ angle.

Step2: Use vertical - angle property for 12

In the second figure (12), $x = 98$ because the angle opposite to the $98^{\circ}$ angle and $x$ are vertical angles. And $y$ is also $98^{\circ}$ as it is vertical to the $98^{\circ}$ angle.

Step3: Use right - angle property for 13

In the third figure (13), since the lines are perpendicular, each of the angles formed is $90^{\circ}$. So $x = 90$ and $y = 90$.

Answer:

1. $x = 81$, $y = 81$
2. $x = 98$, $y = 98$
3. $x = 90$, $y = 90$