Find the value of x. Then classify the triangle by its angle measures.

One angle of the triangle is$45°$.

Second angle is given as$4x°$.

Third angle is given as$5x°$.

Sum of all angles of a triangle is$180°$.

The sum of all the angles of a triangle is$180°$.

This gives us,

$4x{}^{\circ }+5x{}^{\circ }+45{}^{\circ }=180°$

Add both x together.

$9x+45{}^{\circ }=180°$

Subtract 45 from both the sides.

$9x+45{}^{\circ }-45{}^{\circ }=180{}^{\circ }-45°$

This gives us,

$9x=135°$

Now, divide both sides by 9.

$\frac{9x°}{9}=\frac{135°}{9}$

This will give us the value of x.

$x=15°$

Since, the other two angles of the triangle are 4x and 5x.

To find the value of the angle, multiply it with$15°$.

The angle of second side is 4x.

Multiply 4 with 15.

$4x=4\times 15°$

Which gives us the value as$60°$.

The angle of the third side is 5x.

And the value is,

$5x=5\times 15°$

Which gives us the value as$75°$.

The value of x is$x=15°$.

One angle is$45°$, Second angle is $60°$and the third angle is$75°$.

All the three angles of the triangle are different. Hence, it is a scalene right-angled triangle.