ABCD is a cyclic quadrilateral . find the angles of a cyclic quadrilateral .❤❤
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ABCD is a cyclic quadrilateral . find the angles of a cyclic quadrilateral .❤❤
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About a cyclic quadrilateral,
The sum of the two opposite angles is 180°
From figure we get,
Therefore,
From the image,
⇒ ∠B + ∠D = 180° and ∠A + ∠C = 180°
Now,
⇒ 3y - 5 - 7x + 5 = 180 and 4y + 20 - 4x = 180
⇒ 3y - 7x = 180 ....(1)
And 4y - 4x = 160
⇒ y - x = 40 .....(ii) [by dividing RHS and LHS by 4]
On multiplying equation. (ii) by 7 and them by subtracting from the equation. (i), we will get,
→ -4y = 180 - 280
⇒ -4y = -100
⇒ y = 25
Now,
On putting the value of y in equation(i), we will get,
⇒ 25 - x = 40
⇒ -x = 40 - 25
⇒ -x = 15
⇒ x = (-15)
Now put the value of x and y to get the angle values,
= (4*25 + 20)
= 100 + 20
= 120°
= 3*25 - 5
= 75 - 5
= 70°
= -4 * (-15)
= 60°
= -7*(-15) + 5
= 105 + 5
= 110°
Hence,
Angles are
∠A = 120°
∠B = 70°
∠C = 60°
∠D = 110°
Verified answer
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