Question

an exterior angle of a triangle measure 110 and its interior opposite angle are in the ratio 2 ratio 3. find the angle of the triangle​

Answer 1

Answer:Let the 1st angle be 2x and 2nd angle be 3x.

A.T.Q.

2x+3x=110

5x=110

x=110/5

x=22

So,

1st angle=2X22=44

2nd angle=3X22=66

Other angle=180-(44+66)

180-110=70

Step-by-step explanation:

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