If a || b, m∠2 = 63°, and m∠9 = 105°, find the measure of each missing angle.

Given that a || b, m∠2 = 63° and m∠9 = 105°.

Now, all the angles are as follows:

m∠5= m∠2 = 63° [vertically opposite angle]

m∠7= m∠9=105° [vertically opposite angle]

m∠8= 180°-m∠9=180°-105°=75° [Supplementry angles, m∠8+m∠9=180°]

m∠10= m∠8= 180° [vertically opposite angle]

m∠6= m∠8=75° [ Alternate angles]

m∠3= m∠6=75° [vertically opposite angle]

m∠1= 180°-(m∠2+m∠3)=180°-(63°+75°)=42° [as m∠1+m∠2+m∠3=180°]

m∠4= m∠1=42° [vertically opposite angle]

m∠11=m∠4=42° [ Alternate angles]

m∠13= m∠11=42° [vertically opposite angle]

m∠12= 180°-m∠11=180°-42°=138° [as m∠8+m∠9=180°]

m∠14 = m∠12=138° [vertically opposite angle]

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