Question

find the measures of the indicated angles below.
line ( g parallel ) line ( h )
image not drawn to scale

Explanation:

Step1: Find \(m\angle6\)

Since \(\angle6\) and the \(80^{\circ}\) angle are vertical angles, \(m\angle6 = 80^{\circ}\) (vertical angles are equal).

Step2: Find \(m\angle3\)

Because line \(g\parallel\) line \(h\), \(\angle3\) and \(\angle6\) are alternate - interior angles. So \(m\angle3=m\angle6 = 80^{\circ}\) (alternate - interior angles are equal when two parallel lines are cut by a transversal).

Step3: Find \(m\angle2\)

\(\angle2\) and \(\angle3\) are supplementary (\(\angle2+\angle3 = 180^{\circ}\) as they form a linear pair). So \(m\angle2=180 - 80=100^{\circ}\).

Step4: Find \(m\angle1\)

\(\angle1\) and \(\angle2\) are supplementary (\(\angle1+\angle2 = 180^{\circ}\) as they form a linear pair). So \(m\angle1=180 - 100 = 80^{\circ}\).

Step5: Find \(m\angle4\)

\(\angle4\) and \(\angle2\) are vertical angles. So \(m\angle4=m\angle2 = 100^{\circ}\) (vertical angles are equal).

Step6: Find \(m\angle5\)

\(\angle5\) and \(\angle3\) are vertical angles. So \(m\angle5=m\angle3 = 80^{\circ}\) (vertical angles are equal).

Step7: Find \(m\angle7\)

\(\angle7\) and \(\angle6\) are supplementary (\(\angle7+\angle6 = 180^{\circ}\) as they form a linear pair). So \(m\angle7=180 - 80=100^{\circ}\).

Answer:

\(m\angle1 = 80^{\circ}\)
\(m\angle2 = 100^{\circ}\)
\(m\angle3 = 80^{\circ}\)
\(m\angle4 = 100^{\circ}\)
\(m\angle5 = 80^{\circ}\)
\(m\angle6 = 80^{\circ}\)
\(m\angle7 = 100^{\circ}\)