1. **State the problem:** Three angles fit around a point, meaning their sum is 360°. Two of the angles are 112° and 57°. We need to find the size of the third angle and classify it. 2. **Formula used:** The sum of angles around a point is always $$360^\circ$$. 3. **Calculate the third angle:** $$\text{Third angle} = 360^\circ - (112^\circ + 57^\circ)$$ 4. **Simplify inside the parentheses:** $$112^\circ + 57^\circ = 169^\circ$$ 5. **Subtract to find the third angle:** $$\text{Third angle} = 360^\circ - 169^\circ$$ 6. **Show cancellation step:** $$\text{Third angle} = \cancel{360^\circ} - 169^\circ = 191^\circ$$ 7. **Interpret the result:** The third angle is $$191^\circ$$. 8. **Classify the angle:** - Reflex angle: greater than 180° and less than 360° - Obtuse angle: between 90° and 180° - Acute angle: less than 90° - Right angle: exactly 90° Since $$191^\circ > 180^\circ$$, the third angle is a **Reflex** angle. **Final answers:** - a) The third angle is $$191^\circ$$. - b) The third angle is **Reflex**.