Question

question 31
unique id 0663
if a || b || c and m∠9 = 72°, find the measure of each missing angle.

answer
m∠1 =

m∠2 =

m∠3 =

m∠4 =

m∠5 =

m∠6 =

m∠7 =

m∠8 =

m∠10 =

m∠11 =

m∠12 =

Explanation:

Step1: Vertical angles

Vertical angles are equal. So \(m\angle9 = m\angle11=73^{\circ}\)

Step2: Linear - pair angles

\(m\angle9 + m\angle10=180^{\circ}\) (linear - pair). Then \(m\angle10 = 180^{\circ}-73^{\circ}=107^{\circ}\)
Also \(m\angle10 = m\angle12 = 107^{\circ}\) (vertical angles)

Step3: Corresponding angles

Since \(a\parallel b\parallel c\), \(m\angle5=m\angle9 = 73^{\circ}\), \(m\angle6=m\angle10 = 107^{\circ}\), \(m\angle7=m\angle11 = 73^{\circ}\), \(m\angle8=m\angle12 = 107^{\circ}\)

Step4: Alternate - interior angles

\(m\angle1=m\angle5 = 73^{\circ}\), \(m\angle3=m\angle7 = 73^{\circ}\), \(m\angle4=m\angle8 = 107^{\circ}\)

Step5: Linear - pair and vertical angles

\(m\angle1 + m\angle2=180^{\circ}\), so \(m\angle2=180^{\circ}-73^{\circ}=107^{\circ}\)

Answer:

\(m\angle1 = 73^{\circ}\)
\(m\angle2 = 107^{\circ}\)
\(m\angle3 = 73^{\circ}\)
\(m\angle4 = 107^{\circ}\)
\(m\angle5 = 73^{\circ}\)
\(m\angle6 = 107^{\circ}\)
\(m\angle7 = 73^{\circ}\)
\(m\angle8 = 107^{\circ}\)
\(m\angle10 = 107^{\circ}\)
\(m\angle11 = 73^{\circ}\)
\(m\angle12 = 107^{\circ}\)