Question

the measure of one angle of a right triangle is 44ᵒ more than the measure of the smallest angle. find the measures of all three angles.

Answer 1

The smallest angle of the right triangle is 23°, the second angle is 67°, and the right angle is 90°.

Step-by-step explanation:

The student wants to find the measures of all three angles in a right triangle where one angle is 44° more than the measure of the smallest angle. Given that the sum of the angles in any triangle is 180°, and one angle is a right angle (90°), we can set up the following equations: let the smallest angle be x degrees, then the other angle will be x + 44°. The sum of all angles in the triangle is x (smallest angle) + x + 44° (second angle) + 90° (right angle) = 180°. Solving this equation for x gives us the measure of the smallest angle. Once we find x, we simply add 44° to it to find the measure of the second angle.

Solution:

1. x + x + 44° + 90° = 180°
2. 2x + 134° = 180°
3. 2x = 180° - 134°
4. 2x = 46°
5. x = 23°
6. The smallest angle is 23°.
7. The second angle is x + 44° = 23° + 44° = 67°.
8. The right angle is always 90°.

Therefore, the angles of the triangle are 23°, 67°, and 90°.