Question

analyzing angle pair relationships
m∠3 is (3x + 4)° and m∠5 is (2x + 11)°.
angles 3 and 5 are
the equation can be used to
solve for x.
m∠5

Explanation:

Step1: Identify angle relationship

Angles \(3\) and \(5\) are consecutive interior angles. When lines \(p\) and \(q\) are parallel (as indicated by the arrow marks), consecutive interior angles are supplementary. So \(m\angle3 + m\angle5=180^{\circ}\).

Step2: Set up the equation

Given \(m\angle3=(3x + 4)^{\circ}\) and \(m\angle5=(2x + 11)^{\circ}\), the equation is \((3x + 4)+(2x + 11)=180\).
Simplify the left - hand side: \(3x+4 + 2x+11=5x + 15\). So \(5x+15 = 180\).
Subtract \(15\) from both sides: \(5x=180 - 15=165\).
Divide both sides by \(5\): \(x=\frac{165}{5}=33\).

Step3: Find \(m\angle5\)

Substitute \(x = 33\) into \(m\angle5=(2x + 11)^{\circ}\).
\(m\angle5=(2\times33 + 11)^{\circ}=(66+11)^{\circ}=77^{\circ}\).

Answer:

Angles \(3\) and \(5\) are consecutive interior angles. The equation \((3x + 4)+(2x + 11)=180\) can be used to solve for \(x\), and \(m\angle5 = 77^{\circ}\).