Question

1. m∠1 = x + 10 =

m∠2 = 3x + 18 =

Explanation:

Step1: Use the linear - pair relationship

Since \(\angle1\) and \(\angle2\) form a linear pair, \(m\angle1 + m\angle2=180^{\circ}\).
Given \(m\angle1=x + 10\) and \(m\angle2=3x + 18\), we substitute into the equation:
\((x + 10)+(3x + 18)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(x+3x+10 + 18=180\), which gives \(4x+28 = 180\).

Step3: Solve for \(x\)

Subtract 28 from both sides: \(4x=180 - 28\), so \(4x=152\).
Divide both sides by 4: \(x=\frac{152}{4}=38\).

Step4: Find \(m\angle1\)

Substitute \(x = 38\) into \(m\angle1=x + 10\). Then \(m\angle1=38+10=48^{\circ}\).

Step5: Find \(m\angle2\)

Substitute \(x = 38\) into \(m\angle2=3x + 18\). Then \(m\angle2=3\times38+18=114 + 18=132^{\circ}\).

Answer:

\(m\angle1 = 48^{\circ}\), \(m\angle2=132^{\circ}\)