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:

\(x = 15\)