Question

At a charity benefit with 22 people in attendance, three $50 gift certificates are given away as door prizes. Assuming no person receives more than one prize, in how many different ways can the gift certificates be awarded?

Answer 1

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In the Isosceles Triangle ABC,

∠BAC = 30°

So,

∠CBA also = 30° = x (Opposite side in a Isosceles ∆)

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If ∠BAC & ∠CBA = 30°

Then,

∠BAC + ∠CBA + ∠ACB = 180° (Angle Sum Prop. of a Triangle)

➠ 30° + 30° + ∠ACB = 180°

➠ ∠ACB = 180° - 60°

➠ ∠ACB = 120°

If ACB = 120° Then,

∠BCD = 180° - 120°

∠BCD = z = 60°

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If z = 60°

Then,

Y also = 60° (Opp. Sides in an Isosceles ∆ )

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Overall,

x = 30°

y = 60°

z = 60°

.

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