Question

An exterior angle of a triangle measures 110 degree and it's interior opposite angles are in the ratio 2:3.Find of the angles of the triangle​​

Answer 1

Answer:

Exterior angle = 110

Ratio of opposite interior angles = 2:3

Let the angles be 2x and 3x

2x+3x = 110 (exterior angle property)

5x = 110

x = 110/5

x = 22

2x = 22×2 = 44

3x = 22×3 = 66

The two angles are 66 and 44

Let the third angle be y

66+44+y = 180

110+y = 180

y = 180-110

y = 70

The angles of the triangle are 66,44,70

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