In the figure below, AP is parallel to CD. The size w of angle PAB is equal to 135o and the size z of angle DCB is equal to 147o. Find angle ABC.



Asked by Topperlearning User | 14th Oct, 2014, 08:56: AM

Expert Answer:

Draw BS parallel to AP and CD as shown in the figure below.



ABC = ABS + CBS

w' and ABS are alternate interior angles So, ABS = w'

z' and CBS are alternate interior angles So, CBS = z'

Angles w and w' are supplementary which gives w' = 180o - w = 180o - 135o = 45o

Angles z and z' are also supplementary which gives z' = 180o - z = 180o - 147o = 33o

Therefore, we have:

ABC = ABS + CBS

ABC = w' + z' = 45o + 33o = 78o

Answered by  | 14th Oct, 2014, 10:56: AM