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

Question

Philoid · Accepted Answer

It is given that the triangle has its angles as 45°, 64°, and 72°.

On adding these, we get

Sum of three angles = 45° + 64° + 72°

⇒ Sum of three angles = 181°

According to linear pair of axiom, the sum of three angles of the triangle should be equal to 180°.

Since, the sum of the given angles exceeds 180°, no such triangle exists with its angles as 45°, 64°, and 72°.