Question

find the unknown angle​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

x = 35°

y = 40°

Given

∠BAC = 70°

AB = OB

AC = BC

In ΔAOB

OB = AB

∴ ∠OAB = ∠AOB [Opposite angles of equal sides are equal]

i.e. ∠OAB = ∠x

In ΔAOC

BC = AC

∴ ∠BAC = ∠ABC [Opposite angles of equal sides are equal]

Finding ∠y :

∠BAC = ∠ABC

∴ ∠ABC = 70° [∵ ∠BAC = 70°]

In ΔABC

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

⇒ 70° + 70° + ∠y = 180° [∠BCA = ∠Y]

⇒ 140° + ∠BCA = 180°

⇒ ∠BCA = 180° - 140°

⇒ ∠BCA = 40°

i.e. ∠y = 40°

Finding ∠x:

In Δ AOC

   ∠OAC + ∠OCA + ∠AOC = 180° [Angle Sum Property]

⇒ ∠OAB + ∠BAC + ∠ACO + ∠AOC = 180° [∠OAC = ∠OAB + ∠BAC]

⇒ ∠x + 70° + 40° + ∠x = 180° [ ∠AOB = ∠OAB as proved above]

⇒ 2∠x + 110° = 180°

⇒2∠x = 180° - 110°

⇒2∠x = 70°

⇒∠x = $\frac{70}{2}$

⇒∠x = 35°

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