Question

In a cyclic quadrilateral abcd angle a =(2x+4)°, angle b =(4y+4)°, angle c =80° and angle d = 98°. Find the values of x,y and all the angles .

Answer 1

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In a cyclic quadrilateral ABCD, ∠A=(2x+4),∠B=(y+3),∠C=(2y+10),∠D=(4x−5). Find the four angles.

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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°

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Answer 2

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