Question

In the figure given below, OPQR is a rectangle, angle YOQ=90, angle YOP=20 and YO parallel to RZ. Find angles a,b, c and d.


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Answer 1

Answer:

a=70;b=140;c=70;d=90

Step-by-step explanation:

P=Q=QRO=OPQ=90             [sides of a rect.]

YOR=YOP+POR

YOR=90+20=110

YOR=d=110             [alternate interior angles]

d=90

YOP+POQ=90

POQ=90-YOP

POQ=POM=90-20=70

PO//QR              [sides of a rect.]

POQ=a=70               [alternate interior angles]

PM=MO=QO=RO                   [intersecting diagonals of a recta.]

POM=c=70                  [POM is a isosceles triangle]

PQM=90-a

PQM=90-70=20

PQM=MPQ=20               [corresponding angles of equal sides is also equal]

b+PQM+MPQ=180

b=180-(PQM+MPQ)=180-(20+20)=140

b=40