Question

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Answer 1

Answer:

x = 53°

y = 26.5° will be the angle of x and y

Answer 2

$\bf \huge {\underline {\underline \red{AnSwEr}}}$

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Given

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• AB = AC = CD

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• ∠BAC = 84°

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To Find

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• Value of x and y

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Solution

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AB = AC

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So, ∠ABC = ∠ACB [ The angles opposite to the equal sides of a triangle are also equal ]

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Let ∠ABC and ∠ACB be x.

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➞ ∠BAC + ∠ABC + ∠ACB = 180° [ Angle Sum Property ]

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➞ 84° + x + x = 180°

➞ 2x + 84° = 180°

➞ 2x = 180° - 84°

➞ 2x = 96°

➞ x = 96 / 2

➞ x = 48°

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∠ABC = ∠ACB = 48°

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➞∠ACB + ∠ACD = 180° [ Linear Pair ]

➞ 48° + ∠ACD = 180°

➞ ∠ACD = 180° - 48°

➞ ∠ACD = 132°

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CA = CD

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So, ∠CDA = ∠CAD [ The angles opposite to the equal sides of a triangle are also equal ]

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Let ∠CDA and ∠CAD be y.

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➞ ∠ACD + ∠CDA + ∠CAD = 180° [ Angle Sum Property ]

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➞ 132° + y + y = 180°

➞ 2y + 132° = 180°

➞ 2y = 180° - 132°

➞ 2y = 48°

➞ y = 48/ 2

➞ y = 24°

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Therefore, value of x = 48° and y = 24°.