Question

find the values of x and y.
(4y + 10)°
(3y)°
118°
x°
x

y =

Explanation:

Step1: Use angle - addition property

We know that \(118^{\circ}=x^{\circ}+3y^{\circ}\), so \(x = 118 - 3y\).

Step2: Use vertical - angles and straight - angle property

\(\angle BGC\) and \(\angle DGF\) are vertical angles. Also, \(\angle BGC+\angle BGF = 180^{\circ}\) (a straight - angle). Since \(\angle BGC=(4y + 10)^{\circ}\) and \(\angle BGF\) is part of the angle - relationship we can use the fact that the sum of angles around a point is \(360^{\circ}\). But we can also use the linear - pair property. \(\angle BGC\) and \(\angle BGF\) form a linear pair. So \(4y+10 + 118=180\).

Step3: Solve for \(y\)

\[

$$\begin{align*} 4y+10 + 118&=180\\ 4y+128&=180\\ 4y&=180 - 128\\ 4y&=52\\ y& = 13 \end{align*}$$

\]

Step4: Solve for \(x\)

Substitute \(y = 13\) into \(x=118 - 3y\). Then \(x=118-3\times13=118 - 39 = 79\).

Answer:

\(x = 79\), \(y = 13\)