Question

find the values of x and y. (3x - 16)° y° (5x - 110)° x = y =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, \(3x - 16=5x - 110\).

Step2: Solve for \(x\)

\[

$$\begin{align*} 3x-16&=5x - 110\\ 110 - 16&=5x-3x\\ 94&=2x\\ x& = 47 \end{align*}$$

\]

Step3: Find \(y\)

Since \(y\) and \((3x - 16)\) are supplementary (linear - pair of angles, sum is \(180^{\circ}\)). First, find the value of \(3x - 16\) when \(x = 47\). \(3x-16=3\times47-16=141 - 16 = 125\). Then \(y=180-(3x - 16)=180 - 125 = 55\).

Answer:

\(x = 47\)
\(y = 55\)