Question

find the measure of each numbered angle.
questions
110°
30°
130°
m∠1 = °, m∠2 = °, m∠3 = °, m∠4 = °, m∠5 =
°, m∠6 = °, m∠7 = °, m∠8 = °

Explanation:

Step1: Find \(m\angle2\)

Use the property that adjacent angles forming a linear pair sum to \(180^{\circ}\). So \(m\angle2 = 180^{\circ}- 130^{\circ}=50^{\circ}\)

Step2: Find \(m\angle1\)

Use the triangle - angle sum property. Let's assume the triangle with angles \(m\angle1\), \(m\angle2\), and \(30^{\circ}\). Since the sum of angles in a triangle is \(180^{\circ}\), \(m\angle1=180^{\circ}-30^{\circ}-50^{\circ} = 100^{\circ}\)

Step3: Find \(m\angle3\)

Use the vertical - angle property. \(m\angle3\) and the angle adjacent to \(m\angle1\) (which is \(180^{\circ}-100^{\circ} = 80^{\circ}\)) form a vertical - angle pair. So \(m\angle3=80^{\circ}\)

Step4: Find \(m\angle4\)

Use the vertical - angle property. \(m\angle4\) and \(m\angle2\) (\(50^{\circ}\)) form a vertical - angle pair. So \(m\angle4 = 50^{\circ}\)

Step5: Find \(m\angle5\)

Use the vertical - angle property. \(m\angle5\) and \(30^{\circ}\) form a vertical - angle pair. So \(m\angle5=30^{\circ}\)

Step6: Find \(m\angle6\)

Use the vertical - angle property. \(m\angle6\) and \(m\angle4\) (\(50^{\circ}\)) form a vertical - angle pair. So \(m\angle6 = 50^{\circ}\)

Step7: Find \(m\angle7\)

Use the property that adjacent angles forming a linear pair sum to \(180^{\circ}\). So \(m\angle7=180^{\circ}-110^{\circ}=70^{\circ}\)

Step8: Find \(m\angle8\)

Use the triangle - angle sum property. Consider the triangle with angles \(m\angle6\), \(m\angle7\), and \(m\angle8\). Since the sum of angles in a triangle is \(180^{\circ}\), \(m\angle8=180^{\circ}-50^{\circ}-70^{\circ}=60^{\circ}\)

Answer:

\(m\angle1 = 100^{\circ}\), \(m\angle2 = 50^{\circ}\), \(m\angle3 = 80^{\circ}\), \(m\angle4 = 50^{\circ}\), \(m\angle5 = 30^{\circ}\), \(m\angle6 = 50^{\circ}\), \(m\angle7 = 70^{\circ}\), \(m\angle8 = 60^{\circ}\)