Question

an exterior angle of a triangle measures 110 degree and its interior opposite angles are in the ratio 2:3 find the angles

Answer 1

hey look it is the property of triangle that ....
measure of exterior angle of a triangle is the sum of other two non adjecent angles of triangle .....
so the sum of 2 angles must measure up to 110°
so let X be the common multiple
so 2x+3x= 110
5x=110
X=110/5=22...
so 1st angle is 22*2=44
and 2nd is 22*3=66

Answer 2

Step-by-step explanation:

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