In a right _angled triangle one of the acute angles is 20 dgrees greater than the other.find the angles of the triangle
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smaller of the acutes --- x
larger of the acutes --- x+20
but x + x+20 = 90
2x = 70
x = 35
so the angles are 90°, 35° and 55°
Let's assume 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, the second acute angle can be represented as (x + 20) degrees.
In a right-angled triangle, the sum of the acute angles is 90 degrees.
Using this information, we can set up an equation:
x + (x + 20) = 90
Simplifying the equation, we get:
2x + 20 = 90
Subtracting 20 from both sides, we have:
2x = 70
Dividing both sides by 2, we get:
x = 35
So, the first acute angle is 35 degrees.
The second acute angle is (35 + 20) = 55 degrees.
Therefore, the angles of the right-angled triangle are:
35 degrees, 55 degrees, and 90 degrees.
To find the angles of the triangle, we can set up an equation based on the given information. Let's denote the acute angle as x. According to the problem, one of the acute angles is 20 degrees greater than the other:
So, the other acute angle would be x + 20 degrees.
Since we have a right-angled triangle, the sum of the two acute angles must be 90 degrees.
Therefore, we can set up the equation:
x + (x + 20) = 90
Simplifying the equation:
2x + 20 = 90
Subtracting 20 from both sides:
2x = 70
Dividing by 2:
x = 35
So, one of the acute angles is 35 degrees.
The other acute angle can be found by adding 20 to this: 35 + 20 = 55 degrees.
Therefore, the angles of the triangle are 35°, 55°, and 90°.