Question

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, \(7x + 27=10x - 6\).
Solve for \(x\):
\(27 + 6=10x - 7x\)
\(33 = 3x\)
\(x = 11\)

Step2: Find the measure of \((7x + 27)^{\circ}\)

Substitute \(x = 11\) into \(7x+27\):
\(7\times11 + 27=77 + 27=104^{\circ}\)

Step3: Use linear - pair property

\((7x + 27)^{\circ}\) and \((9y - 5)^{\circ}\) form a linear pair (sum to \(180^{\circ}\)).
So, \(104+(9y - 5)=180\)
\(9y+99 = 180\)
\(9y=180 - 99\)
\(9y = 81\)
\(y = 9\)

Answer:

A. 9