If the measures of the acute angles of a right triangle are 3x + 4 degrees and 4x + 2 degrees, what are the measures of all three angles of the right triangle?

Well, you said it was a right-angled triangle, so the largest angle is 90°

the sum of the other two must be 90°
3x+4 + 4x+2 = 90

solve this simple equation for x, then sub in the 2 different expressions

To find the measures of all three angles of the right triangle, we need to remember that the sum of the measures of the angles in any triangle is always 180 degrees.

In a right triangle, one of the angles is always 90 degrees. Therefore, the sum of the two acute angles in a right triangle is equal to 90 degrees.

We are given the measures of the two acute angles as 3x + 4 degrees and 4x + 2 degrees. So, we can set up the equation:

(3x + 4) + (4x + 2) = 90

Simplifying the equation:

7x + 6 = 90

Subtracting 6 from both sides:

7x = 84

Dividing both sides by 7:

x = 12

Now that we have found the value of x, we can substitute it back into the expressions for the acute angles to find their measures:

First acute angle = 3x + 4 = 3(12) + 4 = 36 + 4 = 40 degrees
Second acute angle = 4x + 2 = 4(12) + 2 = 48 + 2 = 50 degrees

Therefore, the measures of all three angles of the right triangle are:

First acute angle = 40 degrees
Second acute angle = 50 degrees
Right angle = 90 degrees