1.

Find the four angles of a cyclic quadrilateral ABCD in which ZA = 2x – 1°, ZB = y + 5°,ZC = 2y + 15º and ZD = 4x - 7º.1​

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ANSWER:

Answer

We KNOW that the sum of the opposite angles of a cyclic QUADRILATERAL is 180

o

. In the cyclic quadrilateral ABCD, angles A and C and the angle B and D form pairs of opposite angles.

∴∠A+∠C=180

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and ∠B+∠D=180

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⇒2x−1+2y+15=180

and y+5+4x−7=180

⇒2x+2y=166

and 4x+y=182

⇒x+y=83 ..(i)

and, 4x+y=182 ..(ii)

Subtracting equation (i) from equation (ii), we get

3x=99⇒x=33

Substituting x=33 in equation (i), we get y=50

Hence, ∠A=(2×33−1)

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=65

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,∠B=(y+5)

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=(50+5)

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=55

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∠C=(2y+15)

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=(2×50+15)

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=115

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and ∠D=(4×33−7)

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=125

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