Find the larger angle between the bisector of an acute angle of a right triangle and the opposite

Find the larger angle between the bisector of an acute angle of a right triangle and the opposite leg if the second acute angle is 26 degrees

Let us denote the problem by letters for convenience. There is a right-angled triangle with right angle C. BK is the bisector of angle B. Angle A = 26 °. Find the angle BKS.

The angles in any triangle add up to 180 °. Then the angle B is equal to:

∠ В = 180 ° – ∠ С – ∠ А = 180 ° – 90 ° – 26 ° = 90 ° – 26 ° = 64 °.

Since BK is the bisector of angle B, it means:

∠ КBС = ∠ КBА = 64 ° / 2 = 32 °.

Let’s find the angle BKС:

∠ BKS = 180 ° – ∠ С – ∠ КBС = 180 ° – 90 ° – 32 ° = 90 ° – 32 ° = 58 °.

Answer: 58 °