For an isosceles triangle ABC- AB-BC - A-2x- - B-x- then - C-

Δ ABC is an isosceles triangle and AB=AC ⇒∠ B=∠ C=x^∘. nbsp;Now, using angle sum proeprty of Δ ABC. ∠ A+∠ B+∠ C=180^∘ ⇒ 2x^∘+x^∘+x^∘=180^∘ ⇒ 4x^∘=180^∘⇒ x=45 ...

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Standard VII

Mathematics

Properties of an Isosceles Triangle

For an isosce...

Question

For an isosceles triangle $A B C, A B = B C & ∠ A = 2 x^{\circ}, ∠ B = x^{\circ}$ , then $∠ C =$

60^{\circ}

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45^{\circ}

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30^{\circ}

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Solution

The correct option is B $45^{\circ}$
$Δ A B C$ is an isosceles triangle and $A B = A C$
$\Rightarrow ∠ B = ∠ C = x^{\circ}$ .
Now, using angle sum proeprty of $Δ A B C$ .
$∠ A + ∠ B + ∠ C = 180^{\circ}$
$\Rightarrow 2 x^{\circ} + x^{\circ} + x^{\circ} = 180^{\circ}$
$\Rightarrow 4 x^{\circ} = 180^{\circ} \Rightarrow x = 45^{\circ}$
$\Rightarrow ∠ C = x^{\circ} = 45^{\circ}$

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