# Find the acute angles of a right-angled triangle if their values are proportional to the numbers 4 and 5.

July 28, 2021 | education

| Let ABC be a right-angled triangle, angle C = 90 degrees, angle A: angle B = 4: 5.

Let x be the coefficient of proportionality, then the angle A = 4x, the angle B = 5x.

By the theorem on the sum of the angles of a triangle:

angle A + angle B + angle C = 180 degrees;

4x + 5x + 90 = 180;

9x = 90;

x = 90/9;

x = 10.

Angle A = 4x = 4 * 10 = 40 degrees, angle B = 5x = 5 * 10 = 50 degrees.

Answer: angle A = 40 degrees, angle B = 50 degrees.

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