Question

using the diagram above, find the value of the angles below using the relationships with \\( \angle 7 \\).
\\( m \angle 1= \\)
\\( m \angle 2= \\)
\\( m \angle 3= \\)
\\( m \angle 5= \\)
\\( m \angle 6= \\)

Explanation:

Step1: Find \(m\angle1\)

\(\angle1\) and \(\angle7\) are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal. So \(m\angle1 = m\angle7=50^{\circ}\)

Step2: Find \(m\angle2\)

\(\angle2\) and \(\angle7\) are supplementary angles (they form a linear pair). So \(m\angle2=180^{\circ}-m\angle7 = 180 - 50=130^{\circ}\)

Step3: Find \(m\angle3\)

\(\angle3\) and \(\angle7\) are alternate - interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal. So \(m\angle3 = m\angle7 = 50^{\circ}\)

Step4: Find \(m\angle5\)

\(\angle5\) and \(\angle7\) are vertical angles. Vertical angles are equal. So \(m\angle5=m\angle7 = 50^{\circ}\)

Step5: Find \(m\angle6\)

\(\angle6\) and \(\angle7\) are supplementary angles (they form a linear pair). So \(m\angle6=180^{\circ}-m\angle7=180 - 50 = 130^{\circ}\)

Answer:

\(m\angle1 = 50\)
\(m\angle2=130\)
\(m\angle3 = 50\)
\(m\angle5=50\)
\(m\angle6 = 130\)