1. **Problem statement:** Find the missing angles \(\angle 1\) and \(\angle 2\) in each figure and provide a reason for the answer. ### Part a) 2. The figure shows a V-shaped angle with one internal angle marked as 50°. 3. The two lines crossing at the vertex form a straight line, so the sum of angles on a straight line is 180°. 4. \(\angle 1\) and the 50° angle are adjacent and form a straight line, so: $$\angle 1 + 50^\circ = 180^\circ$$ 5. Solving for \(\angle 1\): $$\angle 1 = 180^\circ - 50^\circ = 130^\circ$$ 6. \(\angle 2\) is vertically opposite to the 50° angle (formed by the crossing lines), so: $$\angle 2 = 50^\circ$$ 7. **Reason:** Vertically opposite angles are equal. ### Part b) 8. The figure is a triangle with one angle marked 30°, and two segments intersecting inside the triangle creating angles \(\angle 1\) and \(\angle 2\). 9. \(\angle 1\) and \(\angle 2\) are adjacent angles formed by the intersection of two lines, so they are supplementary: $$\angle 1 + \angle 2 = 180^\circ$$ 10. Since the problem does not provide additional angle measures, the best we can say is that \(\angle 1\) and \(\angle 2\) are supplementary. **Final answers:** - a) \(\angle 1 = 130^\circ\), \(\angle 2 = 50^\circ\) - b) \(\angle 1 + \angle 2 = 180^\circ\) (supplementary angles) **Reasons:** - a) Straight line angles sum to 180°, vertically opposite angles are equal. - b) Adjacent angles on a straight line formed by intersecting segments sum to 180°.