Question

48. In the given figure (not drawn to scale),
ABCD and WXYZ both are rhombus,
2 semi-circles and 2 identical triangles are
drawn on the sides of rhombus WXYZ.
Which of the following options is correct?
X Х
cm
A
3 cm
D
W
B
11 cm
4 cm
С
8 cm
Z
P​

Answer 1

Step-by-step explanation:

BAD=∠DCB=72

∘

opposite angles in a rhombus are equal

∠GCF=∠DCB=72

∘

vertically opposite angles

ΔFIH is a equilateral triangle

⇒∠HFI=60

∘

⇒∠GFC=∠HFI=60

∘

vertically opposite angles

given that EC parallel to FG and FC is transversal

⇒∠GFC=∠y=60

∘

ailternate interior angles

In ΔGFC

sum of all angles of a triangle =180

∘

⇒∠x+∠GFC+∠GCF=180

∘

⇒∠x+72

∘

+60

∘

=180

∘

⇒∠x=48

∘

Answered By

toppr

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