17. In the given figure, AB || CD and EF || GH. Find the values of x, y, z and t.
Answers
Step-by-step explanation:
From the figure we know that ∠PRQ=x
o
=60
o
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 angles
so we get
∠PRQ=∠RQS
∠x=∠y=60
o
We know that AB∥CD and PR is a tranversal from the figure we know that ∠PRD and ∠APR are alternate angles
So we get
∠PRD=∠APR
it can be written as
∠PRQ+∠QRD=∠APR
by substituting the values we get
x+∠QRD=110
o
60
o
+∠QRD=110
o
∠QRD=50
o
according to the △QRS
we can write
∠QRD+∠QSR+∠RQS=180
o
by substituting the values
∠QRD+t
o
+y
o
=180
o
50
o
+t
o
+60
o
=180
o
t
o
=70
o
we know that AB∥CD and GH is a transversal from the figure we know that z
o
and t
o
are alternate angles
so we get
z
o
=t
o
=70
o
therefore the values of x,y,z,t are 60
o
,60
o
,70
o
,70
o