To solve the problem, we will compose and solve the equation. But first of all, let’s analyze the condition of the problem.
It says that one of the acute angles of a right-angled triangle is 4/5 of the second.
That is, the triangle is rectangular, so one of its angles is 90 °. The second is denoted by x °, and the third by 4 / 5x °.
The angles of a triangle add up to 180 °.
We get the equation:
90 + x + 4 / 5x = 180;
x + 4 / 5x = 180 – 90;
1.8x = 90;
x = 90: 1.8;
x = 50 ° second angle and 50 ° * 0.8 = 40 °.
Answer: 50 ° and 40 ° are the degree measures of the two angles of the triangle.
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