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

July 28, 2021 | education

| **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.

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