Question

PQRS is a cyclic quadrilateral if angle P minus R equal to 36 and PQ parallel RS, then find all the angles

Answer 1

In a cyclic quadrilateral, the opposite angles add up to 180 degrees

P + R = 180 -------- (i)

But, P - R = 36 ------ (ii)

⇒ P = 36 + R 

Substitute this in (i)

36 + R + R = 180

2R = 144

R = 72

P = 36 + R = 72 + 36 = 108

Since PQ is parallel to SR, we take QR as a transversal

Angle Q and angle R are co-interior angles, they add up to 180

⇒ Q = 180 - 72 = 108


Likewise, PS is a transversal

P + S = 180

S = 180 - 108 = 72


The angles are:

P = 108 degrees

Q = 108 degrees

R = 72 degrees

S = 72 degrees

Answer 2

Answer:

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