Question

3 find the value of y. (7x + 27)° (10x - 6)° (9y - 5)° a) 9 doing the limbo b) 10 swimming laps c) 11 tap dancing d) 12 making smores e) 13 playing volleyball

Explanation:

Step1: Use vertical - angles property

Vertical angles are equal. So, \(7x + 27=10x - 6\).
\[

$$\begin{align*} 7x+27&=10x - 6\\ 27 + 6&=10x-7x\\ 33&=3x\\ x& = 11 \end{align*}$$

\]

Step2: Use another vertical - angles relationship

The angle \((7x + 27)^{\circ}\) is vertical to \((9y - 5)^{\circ}\). First, find the value of \(7x+27\) when \(x = 11\). \(7x+27=7\times11 + 27=77+27 = 104\). Then set \(9y-5=104\).
\[

$$\begin{align*} 9y-5&=104\\ 9y&=104 + 5\\ 9y&=109\\ y&=12 \end{align*}$$

\]

Answer:

D. 12