Math, asked by meenakshireddy6523, 1 year ago

An exterior angle of a triangle measures 110 degree and its interior opposite angles are the ratio2:3. Find the angles of the triangle.

Answers

Answered by Yash2408
0

x =22 tis is the answer

Answered by Anonymous
3

Let the interior opposite angles of triangle are 2x and 3x respectively.

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

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Exterior angle of a triangle is equal to the sum of its interior opposite angles.

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Therefore,

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:\implies\sf 2x + 3x = 110^{\circ} \\\\\\:\implies\sf 5x = 110^{\circ} \\\\\\:\implies\sf  x = \cancel\dfrac{110^{\circ}}{5}\\\\\\:\implies{\underline{\boxed{\sf{x = 22}}}}

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Hence, the interior opposite angles of triangle are:

2x = 2(22) = 44°

3x = 3(22) = 66°

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

Sum of all angles of the triangle is 180°.

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Therefore,

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:\implies\sf 44^{\circ} + 66^{\circ} + \angle C = 180^{\circ}\\\\\\:\implies\sf  110^{\circ} + \angle C = 180^{\circ}\\\\\\:\implies\sf \angle C = 180^{\circ} - 110^{\circ}\\\\\\:\implies{\underline{\boxed{\sf{\pink{\angle C =   70^{\circ}}}}}}\;\bigstar

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\therefore{\underline{\sf{Hence, \; angles\; of \; the \; \triangle \; are\; \bf{44^{\circ}, 66^{\circ} \;\&\; 70^{\circ} }.}}}

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