Page 10 - Ans Sub

12. In the given figure, AB || CD and EF || GH. Find the values of x, y, z and t.

Solution:
0
0
From the figure, we know that ∠PRQ = x = 60 as the vertically opposite angles
are equal.
We know that EF || GH and RQ is a transversal.
From the figure we also know that ∠PRQ and ∠RQS are alternate interior angles
So, we get
∠PRQ = ∠RQS
0
∠x = ∠y = 60
We know that AB || CD and PR is a transversal
From the figure we know that ∠PRD and ∠APR are alternate angles
So, we get
∠PRD = ∠APR
∠PRQ + ∠QRD = ∠APR
0
x + ∠QRD = 110
0
0
60 + ∠QRD = 110
0
0
∠QRD = 110 - 60
0
∠QRD = 50
Now , in △ QRS,
0
∠QRD + ∠QSR + ∠RQS = 180
0
0
0
∠QRD + t + y = 180
0
0
0
0
50 + t + 60 = 180
0
0
0
t= 180 - 50 - 60
0
0
t = 180 – 110
0
0
t = 70
We know that AB || CD and GH is a transversal
0
From the figure we know that z and to are alternate angles
So, we get
0
0
0
z = t = 70
0
0
0
0
Therefore, the values of x, y, z and t are 60 , 60 , 70 and 70 .

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