Question

an exterior angle of a triangle is 110 degree and its interior and closet angles are in the ratio 2 ratio 3 find the angle of the triangle

Answer 1

An exterior angle of an triangle is 110 and its interior opposite angles ar. An exterior angle of an triangle is 110 and its interior opposite angles are in ratio 2:3 find the ...

Answer 2

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