Question

if one angle of a cyclic quadrilateral is acute then the opposite angle is
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Answer 1

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•The sum of the opposite angles in cyclic quadrilateral is 180 ∘

∴∠A+∠C=180 ∘

⇒4y+20−4x=180

⇒4y−4x=180−20

⇒4y−4x=160

⇒x−y=−40....... (i)

∠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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