Question

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

Explanation:

Step1: Use corresponding - angles property

Since \(m\parallel n\), the angles \((3x + 5)^{\circ}\) and \((8x+10)^{\circ}\) are corresponding angles, so they are equal. Set up the equation \(3x + 5=8x + 10\).
\[3x+5 = 8x + 10\]

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(5=8x - 3x+10\), which simplifies to \(5 = 5x+10\). Then subtract 10 from both sides: \(5-10=5x\), so \(- 5 = 5x\). Divide both sides by 5, we get \(x=-1\).
\[x=\frac{-5}{5}=-1\]

Step3: Find the value of \(y\)

The angle \((3x + 5)^{\circ}\) and \(y^{\circ}\) are supplementary (linear - pair of angles). First, find the value of \((3x + 5)^{\circ}\) when \(x = - 1\). Substitute \(x=-1\) into \(3x + 5\), we have \(3\times(-1)+5=-3 + 5=2\). Since \((3x + 5)+y = 180\), then \(y=180-(3x + 5)\). Substituting \(x=-1\) gives \(y = 178\).
\[y=180-(3\times(-1)+5)=178\]

Answer:

\(x=-1,y = 178\)