In A Right Angled Triangle,one Of The Acute Angles Is 20degree Greater Than The Other. Find The Angles Of The Triangle.

smaller angle --- x

larger angle --- x+20
x + x+20 + 90 = 180
2x = 70
x = 35

the angles are 35° , 55° and 90°

Construct a right angled triangle having hypotenuse of length 5.6 cm and with one of the acute angles 30

Show working

To find the angles of a right-angled triangle, we can use the fact that the sum of all angles in a triangle is equal to 180 degrees.

Let's suppose that one of the acute angles is represented by x degrees. According to the problem, the other acute angle is 20 degrees greater than x, so it can be represented by (x + 20) degrees.

Since the sum of all angles in a triangle is equal to 180 degrees, we can write the equation as:

x + (x + 20) + 90 = 180

Simplifying this equation, we get:

2x + 110 = 180

Subtracting 110 from both sides, we have:

2x = 70

Dividing both sides by 2, we find:

x = 35

Therefore, one of the acute angles is 35 degrees, and the other acute angle is (35 + 20) = 55 degrees.

The right angle in the triangle is always 90 degrees.

So, the angles of the triangle are:

Right Angle: 90 degrees
Acute Angle 1: 35 degrees
Acute Angle 2: 55 degrees