In the given figure ABCD is square . A line segment DE intersects the side BC at E and the diagonal AC at O such that COD = 100° , ADO = 50° and OEC = x° . Find the value of x
Answers
Answer:
Correct option is B)
Since DX is a line segment, then
∠COD+∠COX=180 {Angle sum property}
⟹∠COX=180−105=75 −(1)
Since ABCD is a square and AC is a diagonal ,
therefore all the angles in a square is 90
∘
each and AC bisects the angle in half. {property}
⟹∠ACB(∠OCX)=
2
90
=45
∘
−(2)
In traingle COX
⟹∠OCX+∠COX+x=180, { sum of angles in a triangle is 180
∘
)
⟹x=180−(45+75) {using eq 1 and 2}
⟹x=60
∘
Answer:
Correct option is B)
Since DX is a line segment, then
∠COD+∠COX=180 {Angle sum property}
⟹∠COX=180−105=75 −(1)
Since ABCD is a square and AC is a diagonal ,
therefore all the angles in a square is 90
∘
each and AC bisects the angle in half. {property}
⟹∠ACB(∠OCX)=
2
90
=45
∘
−(2)
In traingle COX
⟹∠OCX+∠COX+x=180, { sum of angles in a triangle is 180
∘
)
⟹x=180−(45+75) {using eq 1 and 2}
⟹x=60
∘
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SIMILAR QUESTIONS
star-struck
In the given figure, ABCD is a square and ∠PQR=90
o
. If PB=QC=DR, prove that QB=RC
1715366
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Medium
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ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that:
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