Question

given m || n, find the value of x and y. (8x + 13)° m (9x + 10)° (3y + 5)° n

Explanation:

Step1: Use corresponding - angles property

Since \(m\parallel n\), the corresponding angles are equal. So, \(9x + 10=8x + 13\).
\[9x+10 = 8x + 13\]
\[9x-8x=13 - 10\]
\[x = 3\]

Step2: Use linear - pair property

The angles \((9x + 10)^{\circ}\) and \((3y + 5)^{\circ}\) form a linear - pair. Since \(x = 3\), then \(9x+10=9\times3 + 10=27 + 10=37^{\circ}\).
And \(37+(3y + 5)=180\) (because linear - pair angles sum to \(180^{\circ}\)).
\[3y+5=180 - 37\]
\[3y+5 = 143\]
\[3y=143 - 5\]
\[3y=138\]
\[y = 46\]

Answer:

\(x = 3,y = 46\)