In - ABC-if- A- B-125- and- A- C-113-find- A- B-and - C-

Let ∠ A+∠ B=125^∘ and ∠ A+∠ C=113^∘. ⇒∠ A+∠ B+∠ A+∠ C=125^∘+113^∘ ⇒∠ A+∠ B+∠ C+∠ A=238^∘ ∵∠ A+∠ B+∠ C=180^∘ ⇒ 180^∘+∠ A=238^∘ ⇒∠ A=58^∘ ∴ ∠ C=113^∘ ∠ A =113 ...

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Byju's Answer

Standard IX

Mathematics

Triangle and Sum of Its Internal Angles

In Δ ABC,if ∠...

Question

In $Δ A B C$ , if $∠ A + ∠ B = 125^{\circ}$ and $∠ A + ∠ C = 113^{\circ}$ , find $∠ A, ∠ B$ and $∠ C$ .

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Solution

Given $∠ A + ∠ B = 125^{\circ}$ and $∠ A + ∠ C = 113^{\circ}$
Adding both the equations, we get
$\Rightarrow ∠ A + ∠ B + ∠ A + ∠ C = 125^{\circ} + 113^{\circ} \Rightarrow ∠ A + ∠ B + ∠ C + ∠ A = 238^{\circ}$ ....(i)
Since, In a triangle $∠ A + ∠ B + ∠ C = 180^{\circ}$ .....(ii)
Substitute equation(ii) in equation(i), we get
$\Rightarrow 180^{\circ} + ∠ A = 238^{\circ}$
$\Rightarrow ∠ A = 238^{\circ} - 180^{\circ}$
$\Rightarrow ∠ A = 58^{\circ} ∴ ∠ C = 113^{\circ} - ∠ A = 113^{\circ} - 58^{\circ} = 55^{\circ} ∴ ∠ B = 125^{\circ} - ∠ A = 125^{\circ} - 58^{\circ} = 67^{\circ}$
Hence, $∠ A = 58^{\circ} ∠ B = 67^{\circ} ∠ C = 55^{\circ}$

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In ΔABC, if ∠A+∠B=125∘ and ∠A+∠C=113∘, find ∠A,∠B and ∠C.

In $Δ A B C$ , if $∠ A + ∠ B = 125^{\circ}$ and $∠ A + ∠ C = 113^{\circ}$ , find $∠ A, ∠ B$ and $∠ C$ .