Question

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Answer 1

22) Given : (2 , -1) is a solution of the equation $3x-7y+k = 0$

⇒  $3*2 - 7*-1 + k=0$

⇒ $k = -6 -7$

  ∴ $k = - 13$

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23) Given : in ΔABC , ∠BAC = 64° ; ∠ABC = 50°

We know the sum of the angles in a triangle is 180°

⇒ ∠ABC + ∠ACB + ∠BAC = 180°

⇒ 50° + ∠ACB + 64° = 180°

⇒ ∠ACB = 180° - 114°

⇒ ∠ACB = 66°

∵ Angles B & C are bisected

∠OBC = ∠ABC / 2 = 50°/2

⇒ ∠OBC = 25°

Also, ∠OCB = ∠ACB / 2 = 66°/2

⇒ ∠OCB = 33°

Now in ΔOBC,

∠OBC + ∠OCB + ∠BOC = 180° (∵sum of the interior angles of triangle)

⇒ 25° + 33° + ∠BOC = 180°

 ⇒ ∠BOC = 180 - 58°

   ∴ ∠BOC = 122°