Question

ABCD s a cyclic quadrilateral, if ∠A = 4x, ∠B= 3y, ∠C= 5x, and ∠D= 7y, then x and y are equal to--​

Answer 1

Step-by-step explanation:

Let ABCD be a cyclic quadrilateral.

∠A=2x+4,∠B=y+3,∠C=2y+10,∠D=4x−5

In cyclic quadrilateral the sum of the opposite angles in 180°. Therefore,

∠A+∠C=180°

⇒2x+4+2y+10=180°

⇒2x+2y=166°

⇒x+y=83°→1

∠B+∠D=180°

⇒y+3+4x−5=180°

⇒4x+y=182°→2

Solving 1 and 2, we get

4x+y−x−y=182°−83°⇒3x=99°⇒x=33°

& 33°+y=83°⇒y=83°−33°=50°

∴∠A=2×33°+4=70°,∠B=50°+3=53°

∠C=2×50°+10=110°,∠D=4×33°−5=127°

Answer 2

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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°

Step-by-step explanation:

hope it's help you!!!!!