Question

team names: anissa reid, amase martin, alphea soco
finding angle measures with parallel lines
a. draw this image on your white board
b. work with your team to find the angle measures of angles 1 - 6.
● ( mlt1=)
● ( mlt2=)( mlt3=)( mlt4=)( mlt5=)( mlt6=)

Explanation:

Step1: Find \(m\angle1\)

Use the angle - sum property of angles around a point. The sum of angles around a point is \(180^{\circ}\).
\(m\angle1 + 110^{\circ}=180^{\circ}\)
\(m\angle1=180^{\circ}- 110^{\circ}=70^{\circ}\)

Step2: Find \(m\angle2\)

Use the angle - sum property of angles around a point. The sum of angles around a point is \(180^{\circ}\).
\(m\angle2+115^{\circ}=180^{\circ}\)
\(m\angle2 = 180^{\circ}-115^{\circ}=65^{\circ}\)

Step3: Find \(m\angle3\)

Since \(q\parallel m\) and they are cut by a transversal, \(m\angle2=m\angle3\) (alternate interior angles).
\(m\angle3 = 65^{\circ}\)

Step4: Find \(m\angle4\)

\(m\angle4 + m\angle3=180^{\circ}\) (linear - pair angles)
\(m\angle4=180^{\circ}-m\angle3\)
Substitute \(m\angle3 = 65^{\circ}\), \(m\angle4=115^{\circ}\)

Step5: Find \(m\angle6\)

Use the angle - sum property of angles around a point. The sum of angles around a point is \(180^{\circ}\).
\(m\angle6+45^{\circ}=180^{\circ}\)
\(m\angle6 = 135^{\circ}\)

Step6: Find \(m\angle5\)

Since \(q\parallel m\) and they are cut by a transversal, \(m\angle6=m\angle5\) (alternate interior angles)
\(m\angle5 = 135^{\circ}\)

Answer:

\(m\angle1 = 70^{\circ}\), \(m\angle2=65^{\circ}\), \(m\angle3 = 65^{\circ}\), \(m\angle4=115^{\circ}\), \(m\angle5 = 135^{\circ}\), \(m\angle6=135^{\circ}\)