In a right-angled triangle, the bisector of a smaller angle forms angles with a smaller

In a right-angled triangle, the bisector of a smaller angle forms angles with a smaller leg, one of which is 20 degrees less than the other. Find the sharp corners of the triangle.

The BDC angle is adjacent to the BDA angle, the sum of which is 180.

Angle BDC + BDA = 180.

By condition, the angle ВDА = ВDC + 20.

Then BDC * BDC + 20 = 180.

2 * ВDC = 160.

ВDC = 160/2 = 80.

The CBD triangle is rectangular, then the angle CBD = (90 – BDC) = (90 – 80) = 10.

Since BD is a bisector, then ABC = 2 * CBD = 2 * 10 = 20.

Then the angle BAC = (90 – ABC) = (90 – 20) = 70.

Answer: The acute angles of the triangle are 20 and 70.