Question

10. In the given figure line AB and CD intersect at O. ZBOC = 36º. Find Zx, Zy and Zz.
B
P
Z
36°
2x
у
yo
Z
90°
x
KR
D
T
Fig. Q. 10
Fig. Q. 11
11. In the given figure, PQ and RS are two lines intersecting each other at point 'O'. If ZROT = 90°, find
the value of x, y and z.
​

Answer 1

Answer:

In the given figure line AB and CD intersect at O . ∠BOC=36

∘

. Find ∠x , ∠y and ∠z

1102900

Medium

Answer

In first figure,

∠AOD=∠BOC ------- Vertically Opposite angles

∴x=36

∘

∠AOC+∠COB=180

∘

------ Angles on straight line

y+36

∘

=180

∘

y=180

∘

−36

∘

y=144

∘

∠AOC=∠BOD ------- Vertically Opposite angles

y=z=144

∘

In second figure,

∠POR+∠ROT+∠QOT=180

∘

------ Angles on straight line

2x+90

∘

+x=180

∘

3x=90

∘

x=30

∘

∴2x=60

∘

∠POR=∠SOQ ------- Vertically Opposite angles

2x=y=60

∘

∠POS=∠ROQ ------- Vertically Opposite angles

z=90

∘

+x

z=90

∘

+30

∘

z=120

∘