In the given figure, ABCD is a quadrilateral and AO and DO are bisectors of ∠Aand∠D. The value of 'x ' is
A
70∘
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B
85∘
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C
95∘
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D
120∘
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Solution
The correct option is C95∘ In a quadrilateral ABCD, AO and DO are bisectors of ∠A and ∠D.
So, ∠DAO=∠A2 and ∠ADO=∠D2 ∵ Sum of angles in a quadrilateral is 3600 ⇒∠A+∠B+∠C+∠D=360∘ ⇒∠A+∠D+120+70=360∘ ⇒∠A+∠D=170∘ ⇒∠A2+∠D2=85∘ ---------(1)
∵ Sum of angles in a triangle is 1800 ⇒∠A2+∠D2+x=1800 ⇒x=180∘−(∠A∠2+∠D∠2) ⇒x=180∘−85∘ =95∘
Hence, the value of 'x' is 95∘.