Question

In the adjoining figure,AB||QP,BC||RQ and CA||PR, angle AEQ=110° and angle RPQ=50°,find angle A, angle B, angle C, angle Q, angle R​

Answer 1

Answer:

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Draw a line KH passing through the point F which is parallel to both AB and CD

We know that KF∥CD and FG is a transversal

from the figure we know that ∠KFG and ∠FGD are alternate angles

So we get

∠KFG=∠FGD=r

o

...(i)

We also know that AE∥KF and EF is a transversal

from the figure we know that ∠AEF and ∠KFE are alternate angles

So we get

∠AEF+∠KFE=180

o

By substituting the values we get

p

o

+∠KFE=180

o

∠KFE=180

o

−p

o

....(ii)

By adding both the equations (i) and (ii) we get

∠KFG+∠KFE=180

o

−p

o

+r

o

from the figures ∠KFG+∠KFE can be written as ∠EFG

∠EFG=180

o

−p

o

+r

o

We know that ∠EFG=q

o

q

o

=180

o

−p

o

+r

o

It can be written as

p+q−r=180

o

Answer 2

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