Final answer:
To find the measures of all three angles of a right triangle, assign variables to represent the angles and set up an equation. Solve for the smallest angle using the given information and calculate the other angles using the equations. The smallest angle of the right triangle is 23 degrees, the second angle is 67 degrees, and the right angle is 90 degrees.
Step-by-step explanation:
To find the measures of all three angles of a right triangle, let's first assign variables to represent the angles.
Let's say the smallest angle is x degrees. The measure of one angle is 44 degrees more than the smallest angle, so the second angle is x + 44 degrees.
The sum of the angles of a triangle is 180 degrees. Since two angles are known, we can set up an equation:
x + (x + 44) + 90 = 180
Combining like terms, we get 2x + 44 + 90 = 180.
Simplifying further, we have 2x + 134 = 180.
Subtracting 134 from both sides, we get 2x = 46.
Finally, dividing both sides by 2, we find that x = 23 degrees.
Therefore, the smallest angle of the right triangle is 23 degrees, the second angle is 23 + 44 = 67 degrees, and the right angle is 90 degrees.