Question

each of two equal angles of a triangle is twice the third angle find the angles of the triangle​

Answer 1

Given: Each of two equal angles of a triangle is twice the third angle.

To find: The angles of the triangle.

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Let the third angle be x.

$\underline{\boldsymbol{According\: to \:the\: Question :}}$

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• Each of two equal angles of a triangle is twice the third angle.

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$:\implies\sf Each \; angle = 2x$

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$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀⠀

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• Sum of all angles of the triangle is 180°.

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Therefore,

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$:\implies\sf x + 2x + 2x = 180 \\\\\\:\implies\sf 5x = 180 \\\\\\:\implies\sf x = \cancel\dfrac{180}{5}\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 36^{\circ}}}}}}\;\bigstar$

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$\underline{\bf{\dag} \:\mathfrak{Angles\;of\;\triangle\;are\: :}}$⠀⠀

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• First angle, x = 36°.
• Second & third angle, 2x = 2(36) = 72°.

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$\therefore{\underline{\sf{Hence,\; angles \; of \; the \;\triangle\;are\; \bf{36^{\circ}, 72^{\circ}\;\&\;72^{\circ} }.}}}$

Answer 2

Answer:

Given :-

• Each of two equal angles of a triangle is twice the third angles.

To Find :-

• What is the angles of the triangle.

Solution :-

Let, the first angles be x

And, the second angles be 2x

And, the third angles will be 2x

As we know that,

$\sf\bold{\star{\red{Sum\: of\: all\: angles\: if\: a\: triangle =\: 180^{\circ}}}}$

According to the question by using the formula we get,

⇒ $\sf x + 2x + 2x =\: 180^{\circ}$

⇒ $\sf 3x + 2x =\: 180^{\circ}$

⇒ $\sf 5x =\: 180^{\circ}$

⇒ $\sf x =\: \dfrac{\cancel{180^{\circ}}}{\cancel{5}}$

➠ $\sf\bold{\purple{x =\: 36^{\circ}}}$

Hence, the required angles are,

✧ First angles = x = 36°

✧ Second angles = 2x = 2(36°) = 72°

✧ Third angles = 2x = 2(36°) = 72°

$\therefore$ The angles of a triangle is 36°, 72° and 72° respectively.