Question

please answer me fast

Answer 1

To find QPM:

In ∆QPM,

Q + P + M = 180

=> 50 + P + 90 = 180
(M is 90 because PQ is the diameter)

=> 140 + P = 180

=> P = 180 - 140 = 40

=> QPM = 40°
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To find QPR:

QRPM is a cyclic quadrilateral. So sum of opposite angles is 180

=> MPR + MQR = 180

=> MPR + (65+50) = 180

=> MPR = 180 - 65 - 50

=> MPR = 65

=> QPM+ QPR = 65

=> 40 + QPR = 65

=> QPR = 65 - 40

=> QPR = 25°
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To find PRS:

PQRS is a cyclic quadrilateral. So sum of opposite angles is 180

=> PSR + PQR = 180

=> PSR + 65 = 180

=> PSR = 180-65 = 115°


Now in ∆PRS,

PRS + RSP + SPR = 180

=> PRS + 115 + 40 = 180

=> PRS = 180 - 115 - 40

=> PRS = 25°