In triangle ABC, if B C = A C and ∠ B = 40 ∘ . Then ∠ C is equal to ___ degrees. Options:

In triangle ABC, if BC=AC and ∠B=40∘. Then ∠C is equal to __

Question

In triangle ABC, if $B C = A C$ and $∠ B = 40^{\circ}$ . Then $∠ C$ is equal to

___ degrees.

Options:

Answer: Option A
:

In a triangle, if two sides are equal then it is an isosceles triangle. The angles opposite to the two equal sides are also equal.

Therefore, $∠ A = ∠ B$

Since sum of all the angles in a triangle $= 180^{\circ}$

$\Rightarrow$ $∠ A + ∠ B + ∠ C = 180^{\circ}$

$\Rightarrow$ $2 \times 40^{\circ} + ∠ C = 180^{\circ}$ ( $∠ A = ∠ B$ )

$\Rightarrow$ $∠ C$ $= 180^{\circ} - 2 \times 40^{\circ}$

$\Rightarrow$ $∠ C$ $= 100^{\circ}$

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