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 the relationship between angles 3 and 5

Angles 3 and 5 are same - side interior angles. But if we assume lines \(p\) and \(q\) are parallel (from the arrow - like markings on \(p\) and \(q\)), then by the property of parallel lines cut by a transversal, angles 3 and 5 are supplementary. So \(m\angle3+m\angle5 = 180^{\circ}\)

Step2: Set up the equation

Given \(m\angle3=(3x + 4)^{\circ}\) and \(m\angle5=(2x+11)^{\circ}\), we substitute into the supplementary - angle equation:
\((3x + 4)+(2x + 11)=180\)
Combine like terms:
\(3x+2x+4 + 11=180\)
\(5x+15 = 180\)
Subtract 15 from both sides:
\(5x=180 - 15\)
\(5x=165\)
Divide both sides by 5:
\(x=\frac{165}{5}=33\)

Step3: Find \(m\angle5\)

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

Answer:

Angles 3 and 5 are supplementary. The equation \((3x + 4)+(2x + 11)=180\) can be used to solve for \(x\). \(m\angle5 = 77\)