Question 28
Triangles and QuadrilateralsIn a triangle XYZ, ∠YXZ = 44° and ∠XYZ = 112°. Calculate the acute angle between the internal bisectors of ∠XYZ and ∠XZY.
- A.12°
- B.56°
- C.68°
- D.78°
Show the answer and explanation
Answer: C (68°)
Explanation
∠XZY = 180° − 44° − 112° = 24°. The bisectors make 56° and 12° with YZ, so they meet at 180° − 56° − 12° = 112°. The acute angle between them is 180° − 112° = 68°.