Question 8:
ABCD is a cyclic quadrilateral finds the angles of the cyclic quadrilateral.
Answer:
We know that the sum of the measures of opposite angles in a cyclic quadrilateral is 180°.
Therefore, ∠A + ∠C = 180
4y + 20 − 4x = 180
− 4x + 4y = 160
x − y = − 40 (i)
Also, ∠B + ∠D = 180
3y − 5 − 7x + 5 = 180
− 7x + 3y = 180 (ii)
Multiplying equation (i) by 3, we obtain
3x − 3y = − 120 (iii)
Adding equations (ii) and (iii), we obtain
− 7x + 3x = 180 − 120
− 4x = 60
x = −15
By using equation (i), we obtain
x − y = − 40
−15 − y = − 40
y = −15 + 40 = 25
∠A = 4y + 20 = 4(25) + 20 = 120°
∠B = 3y − 5 = 3(25) − 5 = 70°
∠C = − 4x = − 4(− 15) = 60°
∠D = − 7x + 5 = − 7(−15) + 5 = 110°
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