Calculate the degree measures of the acute angles of a right triangle if you know that some

Calculate the degree measures of the acute angles of a right triangle if you know that some of them are 26 degrees smaller than the other.

To solve this example, we will use two conditional variables “X” and “Y”, through which we denote the degree values of the larger and smaller acute angles of a rectangular triangle, respectively.

Based on the example data, we will compose the following equations:

1) X + Y = 90;

2) X – Y = 26.

Solving the system of two equations, we get X = 90 – Y.

By inserting X into the second equation, we will have 90 – Y – Y = 26 or 90 – 2Y = 26 or 2Y = 90 – 26 = 64 or Y = 64/2 = 32 ℃.

Therefore, X = 90 – 32 = 58 ℃.

Answer: 58 ℃ and 32 ℃.