Question

find the measure of each numbered angle.

1. ( m angle 2 = 57 )
2. ( m angle 1 = 38 )
3. ( m angle 1 = x + 10 )( m angle 2 = 3 x + 18 )

Explanation:

Step1: Use the linear - pair relationship

For problem 13:
Since \(\angle1\) and \(\angle2\) form a linear pair, \(m\angle1 + m\angle2=180^{\circ}\). Given \(m\angle2 = 57^{\circ}\), then \(m\angle1=180 - 57\).

Step2: Calculate the value

\(m\angle1=123^{\circ}\)

For problem 14:
\(\angle1\) and \(\angle2\) are vertical angles. By the vertical - angles theorem, \(m\angle1=m\angle2\). Given \(m\angle1 = 38^{\circ}\), so \(m\angle2 = 38^{\circ}\)

For problem 15:
Since \(\angle1\) and \(\angle2\) form a linear pair, \(m\angle1 + m\angle2=180^{\circ}\). Substitute \(m\angle1=x + 10\) and \(m\angle2=3x + 18\) into the equation: \((x + 10)+(3x + 18)=180\)

Step3: Solve the equation

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Step4: Find the measure of angles

Substitute \(x = 38\) into \(m\angle1=x + 10\), then \(m\angle1=38+10 = 48^{\circ}\)
Substitute \(x = 38\) into \(m\angle2=3x + 18\), then \(m\angle2=3\times38+18=114 + 18=132^{\circ}\)

Answer:

1. \(m\angle1 = 123^{\circ}\)
2. \(m\angle2 = 38^{\circ}\)
3. \(m\angle1 = 48^{\circ}\), \(m\angle2 = 132^{\circ}\)