Question

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

Answer 1

Step-by-step explanation:

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