ABCD is a cyclic quadrilateral DA = 4x and DC =2x then the value of x
Answers
Answered by
2
In a cyclic quadrilateral ABCD,∠A=(2x+4)
o
,∠B=(y+3)
o
,∠C=(2y+10)
o
and∠D=(4x−5)
o
. Find measure of each angle.
Share
Save
ANSWER
∠A+∠C=180
o
[ Sum of angles in cyclic quadrilateral are supplementary ]
⇒ 2x+4
o
+2y+10
o
=180
o
⇒ 2x+2y=166
o
∴ x+y=83
o
----- ( 1 )
Now, ∠B+∠D=180
o
⇒ y+3
o
+4x−5
o
=180
o
⇒ 4x+y=182
o
---- ( 2 )
Subtracting equation ( 1 ) from equation ( 2 ) we get,
x=33
o
Substituting value of x in equation ( 1 ) we get,
y=50
o
.
⇒ ∠A=(2x+4)
o
=(2×33+4)
o
=70
o
⇒ ∠B=(y+3)
2
=(50+3)
o
=53
o
⇒ ∠C=(2y+10)
o
=(2×50+10)
o
=110
o
⇒ ∠D=(4x−5)
o
=(4×33−5)
o
=127
o
MARK ME THE BRAINLIEST
Similar questions