MATHS Consider the figure shown. What is the measure of Zoyz if the triangle OYZ is an isosceles triangle? SW 3a a- 52a + 11 0 X Z 24.50 69° 34.50 111 Review later Back Na
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In the given figure (not to scale) ABC is an isosceles triangle in which AB = AC. AEDC is parallelogram. If ∠CDF=70
∘
and ∠BFE=100
∘
then find ∠FBA.
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Correct option is
A
40
Given, ABC is an isosceles triangle in which AB = AC
AEDC is a parallelogram
∠CDF=70
∘
and ∠BFE=100
∘
Since AEDC is a parallelogram
∠ACD+70
∘
=180
∘
⇒∠ACD=110
∘
→(1)
⇒∠ACD+∠GCB=180
∘
(∵ linear pair )
⇒∠GCB=180
∘
−110
∘
=70
∘
→(2)
∠GFD+∠BFE=180
∘
(linear pair)
⇒∠GFD=180
∘
−100
∘
=80
∘
→(3)
In ∠BFD,∠FBD=180
∘
−(80
∘
+70
∘
)=30
∘
SinceAB=AC,∠ABC=∠ACB
∴∠ABC=70
∘
⇒∠ABF=∠ABC−∠FBD=70
∘
−30
∘
=40
∘