Question

find the values of x and y.
139°
e
h
(9x - 5)°
k
j
x = 16
y =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. The angle $(9x - 5)^{\circ}$ and the angle opposite to the $139^{\circ}$ angle are vertical angles. The angle opposite to the $139^{\circ}$ angle is $139^{\circ}$ (vertical - angle property). So we set up the equation $9x-5 = 139$.
\[9x-5=139\]

Step2: Solve for x

Add 5 to both sides of the equation: $9x=139 + 5=144$. Then divide both sides by 9: $x=\frac{144}{9}=16$.

Step3: Find the value of y

Since $\angle EKH$ is a straight - line angle, $\angle EKH=180^{\circ}$. We know that one part of $\angle EKH$ is a right - angle ($90^{\circ}$) and the other part is $y^{\circ}$. Also, we can use the fact that the sum of angles around a point is $360^{\circ}$. But a simpler way is to note that $\angle EKH$ is a straight line. So $y + 90=180 - 139$.
\[y=180-139 - 90+90=41\]

Answer:

$y = 41$