Question

fund the letterd in this figure​

Answer 1

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Answer 2

Hey there!

♣ Given Data:

∠QPR = 59°

∠RPS = 32°

♣ Finding angle x by Isosceles Δ Properties:

ΔPQR is isosceles Δ.   ( two sides are equal)

∠RPQ = ∠Q = 59°   (base ∠s of isosceles Δ are equal)

Now,

In ΔPQR,

∠Q + ∠QRP + ∠RPQ = 180° (angle sum property)

59 + x + 59 = 180

x = 180 - 118

x = 62°        ← (Ans)

♣ Applying Straight Line property to get ∠PRS :

∠QRP + ∠PRS = 180°  ( straight line property)

62 + ∠QRP = 180°

∠QRP = 180 - 62

∠QRP = 118°

♣ Applying Angle sum property in ΔPRS :

∠PRS + ∠RPS + ∠S = 180° (angle sum property:)

118 + 32 + y = 180

y = 180 - 118 - 32

y = 180 - 150

y = 30°      ←(Ans)

Hope It helps You!