Question

in the figure, ( mangle3=(5(x + 4)-13)^{circ} ) and ( mangle5=(2x + 3(x + 11))^{circ} )
which value of ( x ) would make line ( p ) parallel to line ( q )?

Explanation:

Step1: Simplify the expressions for \(m\angle3\) and \(m\angle5\)

Simplify \(m\angle3=(5(x + 4)-13)^{\circ}\):

$$
LATEXBLOCK0
$$

Simplify \(m\angle5=(2x+3(x + 11))^{\circ}\):

$$
LATEXBLOCK1
$$

Step2: Use the property of parallel lines (alternate - interior angles)

When \(p\parallel q\), \(m\angle3+m\angle5 = 180^{\circ}\) (same - side interior angles are supplementary).
So, \((5x + 7)+(5x + 33)=180\)

$$
LATEXBLOCK2
$$

Step3: Solve the equation for \(x\)

Subtract \(40\) from both sides: \(10x=180 - 40=140\)
Divide both sides by \(10\): \(x=\frac{140}{10}=14\)

Answer:

\(x = 14\)