Question

ABCD is a cyclic quadrilateral such that angle a = (4y +20)°, angle b = (3y - 5)°, angle c = (4x)°, angle d = (7x + 5)°. find the four angles.​

Answer 1

Answer:

In quadrilateral ABCD,

∠A+∠C=180°

⇒4y+20−4x=180°

−4x+4y=160°

⇒−x+y=40°

⇒−3x+3y=120°→1

∠B+∠D=180°

3y−5+7x+5=180°

7x+3y=180°→2

Solving equation 1 and 2, we get

7x+3y+3x−3y=180°−120°⇒10x=60°⇒x=6

& −6+y=40°⇒y=46°

∴∠A=4×46°+20=204°,∠B=3×46−5=133°

∠C=−4×6=−24°,∠D=7×6+5=47°

solution