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

How many triangles can be drawn having its angles at $53°, 64°$ and $63°$? Give a reason for your answer.

The angles of a triangle are $\left(x-40\right)°, \left(x-20\right)°$ and $\left(\frac{x}{2}-10\right)°$. Find the value of $x$ and the angles of the triangle.

If one angle of a triangle is equal to the sum of the other two angles, then prove that triangle is a right angled triangle.

If the angles of a triangle are in the ratio $2:3:4$, then find the measures of angles of the triangle.

In the figure given below, find $x$:

In the figure given below, find $x$:

In the figure given below, find the values of $x$ and $y$: