an exterior angle of a triangle measures 125 degrees and its interior opposite angles are in the ratio 2 : 3,what are the angles of the triangle?

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Solution

The exterior angle of a triangle equals the sum of its opposite interior angles.

Measure of exterior angles = 125 deg
Ratio of opposite interior angles = 2:3
Let the two angles be 2x and 3x
Now, 2x + 3x = 125 deg
5x = 125 deg
x = 25 deg
2x = 50 deg and 3x = 75 deg
Thus, the measures of the two opposite interior angles = 50 deg and 75 deg
The measure of the third angle is 180 - (50 + 75) = 180 - 125 = 55 deg

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