Question

given m||n, find the value of x. (2x + 5)° (9x + 10)°

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), the two given angles \((2x + 5)^{\circ}\) and \((9x+10)^{\circ}\) are same - side interior angles. Same - side interior angles are supplementary, so their sum is \(180^{\circ}\).
\[2x + 5+9x + 10=180\]

Step2: Combine like - terms

Combine the \(x\) terms and the constant terms on the left - hand side of the equation.
\[ (2x+9x)+(5 + 10)=180\]
\[11x+15 = 180\]

Step3: Isolate the variable term

Subtract 15 from both sides of the equation.
\[11x+15-15=180 - 15\]
\[11x=165\]

Step4: Solve for \(x\)

Divide both sides of the equation by 11.
\[x=\frac{165}{11}\]
\[x = 15\]

Answer:

\(x = 15\)