1. **Problem statement:** Find the measures of the numbered angles in the rhombus given the side lengths and angle markings. 2. **Recall properties of a rhombus:** - All sides are equal in length. - Opposite angles are equal. - Diagonals bisect each other at right angles. - Diagonals bisect the angles of the rhombus. 3. **Given information:** - Sides marked as 3, 2, and 4 in different sections likely represent segments formed by diagonals or angle bisectors. - Angles inside the rhombus include 39°, 60°, 90°, and another 39°. - Angle 1 is given as 60°. 4. **Step-by-step solution:** 1. Since the diagonals bisect the angles, each angle of the rhombus is split into two equal parts. 2. Given angle 1 = 60°, the full angle at that vertex is $$2 \times 60^\circ = 120^\circ$$. 3. Opposite angles in a rhombus are equal, so the angle opposite to angle 1 is also 120°. 4. The sum of adjacent angles in a rhombus is 180°, so the other two angles are: $$180^\circ - 120^\circ = 60^\circ$$ each. 5. Therefore, the four angles of the rhombus are: $$120^\circ, 60^\circ, 120^\circ, 60^\circ$$. 6. The diagonals intersect at right angles (90°), confirming the 90° angle marked inside. 7. The 39° angles likely correspond to angles formed by the diagonals or bisectors but do not affect the main rhombus angles. **Final answer:** - Numbered angle 1 = 60° - The rhombus angles are 120°, 60°, 120°, and 60°.