In the figure given below, AL||EM. Find the measure of all the interior angles cut by the transversals PK and BN.

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

Expert Answer:

Given:-

ACQ = 80o and LDB = 112o

We have to find:-

QCD , ODC , OQC and DOQ

QCD + ACQ = 180o (linear pair of angles)

Thus, QCD = 180o - 80o = 100o

ODC = LDB (pair of vertically opposite angles)

LDB = 112o

Thus, ODC = 112o

ACQ = OQC (pair of alternate interior angles)

ACQ = 80o

Thus, OQC = 80o

Now, DOQ + ODC = 180o (interior angles on the same side of the transversal are supplementary)

DOQ + 112o = 180o

Thus,DOQ = 68o

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