How many triangles can be drawn having its angles as $45 °, 64 °$ and $72 °$ ? Give reason for your answer.

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Solution

Evaluate the number of triangles that can be formed based on given information
According to the angle sum property of a triangle, the sum of interior angles should be $180^{°}$
The sum of the measure of give angles $= 45^{°} + 64^{°} + 72^{°} = 181^{°}$
As the given angles violate the angle sum property of a triangle, no triangles can be drawn with given angles.
Hence, $0$ triangles can be drawn with the given angles.

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