Question

corresponding angles alternate exterior angles alternate interior angles same-side interior angles = or + = 180° x = m∠1 = m∠2 =

Explanation:

Step1: Use the property of same - side interior angles

Since the two angles \(2x + 67\) and \(5x-55\) are same - side interior angles, we know that \((2x + 67)+(5x-55)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2x+5x+67 - 55=180\), which gives \(7x+12 = 180\).

Step3: Solve for \(x\)

Subtract 12 from both sides: \(7x=180 - 12=168\). Then divide both sides by 7: \(x=\frac{168}{7}=24\).

Step4: Find \(m\angle1\)

\(m\angle1=2x + 67\). Substitute \(x = 24\) into the expression: \(m\angle1=2\times24+67=48 + 67=115^{\circ}\).

Step5: Find \(m\angle2\)

First, find \(5x-55\) when \(x = 24\), \(5x-55=5\times24-55=120 - 55 = 65^{\circ}\). Since \(\angle2\) and \(5x - 55\) are vertical angles, \(m\angle2=65^{\circ}\).

Answer:

\(x = 24\), \(m\angle1=115^{\circ}\), \(m\angle2=65^{\circ}\)