An exterior angle of a triangle measures 110° and its interior opposite angles are in the ratio 2 : 3. Find the angles of the triangle.

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Solution

Suppose the interior opposite angles are (2x)° and (3x)°.
We know that the exterior angle of a triangle is equal to the sum of the interior opposite angles.

∴ 3x +2x= 110
x = 22

The interior opposite angles are $(2 \times 22) ° and (3 \times 22) °, i . e .$ 44° and 66°.
Suppose the third angle of the triangle is y°.
Now, sum of the angles in any triangle is 180°.

∴ 44 + 66 + y = 180
y = 70

Hence, the angles of the triangle are 44°, 66° and 70°.

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