Question

In a right triangle, the acute angles measure x + 15 and 2x degrees. What is the measure of the smallest angle of the triangle?

Answer 1

First, solve for each of the angles. Since it is a right triangle, one of the angles is 90 degrees. Knowing that the sum of the angles of a triangle are always equal to 180 degrees, you can write an equation for the triangle.

Angle1+ angle2+angle3=180.

Which means that 90+(x+15)+2x=180.

After finding the value of x, which is 25 in this case, solve for each angle.

X+15=25+15=40.

2x=25*2= 50

The value of the smallest angle is 40 degrees.

Answer 2

In a right triangle, the sum of the measures of the angles is 180 degrees. We know that one of the angles is a right angle, which measures 90 degrees. So, the sum of the other two angles must be 180 - 90, which equals 90 degrees.

The problem tells us that the measures of the two acute angles are x + 15 and 2x degrees. As per what we just discussed, their sum must be equal to 90 degrees. Therefore, we can write the equation:

x + 15 + 2x = 90

Solving this equation for x gives:

3x + 15 = 90
3x = 90 - 15
3x = 75
x = 75 / 3
x = 25 degrees.

Now that we know the value of x, we can calculate the measures of the acute angles. The first one measures x + 15 degrees, so replacing x with 25 gives:

25 + 15 = 40 degrees.

The measure of the second angle is 2x, so substituting x with 25 gives:

2 * 25 = 50 degrees.

Finally, we need to find out which of these two angles is the smallest. As it turns out, the smallest angle measures 40 degrees.