Question

find angles x and y : ​

Answer 1

Answer:

x =45°

y=135°

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Answer 2

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Let ∠RPQ be = 'a'

∵ PQ = QR (given)

∴ ∠PRQ = ∠PRQ

=> x = a

So we can say that ∠RPQ = 'x'

Now, in ∆ PQR

∠RPQ + ∠PQR + ∠RPQ = 180° (Angle sum property of triangle)

Substituting the values,

x + 90° + x = 180°

2x + 90° = 180°

2x = 180° - 90°

2x = 90°

x = $\frac{90°}{2}$

x = 45°

Now,

∠Y = ∠PRQ + ∠PQR (exterior angle property)

∠Y = x + 90°

∠Y = 45° + 90°

∠Y = 135°

Therefore,

• ∠X = 45°
• ∠Y = 135°

Hope it helps......