One of the acute angles of a right-angled triangle is 20 degrees larger than the other acute angle.

One of the acute angles of a right-angled triangle is 20 degrees larger than the other acute angle. find the degree measure of each acute angle.

Let us introduce the notation:

Let the smallest of the acute angles of a right-angled triangle be x0, and then the largest is x + 20.

Let’s compose and solve the equation:

As you know, the sum of the angles of a triangle is 180, so

x + (x + 20) + 90 = 180,

x + x + 20 + 90 = 180,

2x + 110 = 180,

2x = 180 – 110,

2x = 70,

x = 70: 2,

x = 35.

This means that the smaller acute angle is 35.

Find the degree measure of the larger acute angle:

35 + 20 = 55.

Answer: The acute angles of a right-angled triangle are 35 and 55.