Question

In the given fig ABCD is a circumscribed quadrilateral. Find all the angles of quadrilateral​

Answer 1

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x= -15

y= 25

Therefore,

angleA=120

angleB=70

angleC=60

angleD=110

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Answer 2

Answer:

A = 120°

B = 70°

C = 60°

D = 110°

Explanation :

We know that the sum of opposite angles of a quadrilateral in a circle is 180°.

So, 4y + 20 - 4x = 180° and 3y-5 - 7x +5 = 180°

y - x = 40° and 3y - 7x = 180°

y = 40° + x

Putting this value in equation 2,

3( x + 40 ) - 7x = 180

3x + 120 - 7x = 180

- 4x = 60

x = - 15

y = 40 - 15

y = 25

Angle A = 4y + 20 = 4(25) +20 = 120°

Angle B = 3y - 5 = 3(25) - 5 = 70°

Angle C = - 4x = - 4(-15) = 60°

Angle D = - 7(-15) + 5 = 110°