1. **Problem statement:** Find the measures of the numbered angles 1, 2, 3, and 4 inside the rhombus, given one angle of the rhombus is 39°. 2. **Key properties of a rhombus:** - All sides are equal. - Opposite angles are equal. - Adjacent angles are supplementary (sum to 180°). - Diagonals are perpendicular (intersect at 90°). - Diagonals bisect the angles of the rhombus. 3. **Step 1: Find the opposite angle to 39°** Since opposite angles are equal, the angle opposite 39° is also 39°. 4. **Step 2: Find the adjacent angles** Adjacent angles are supplementary, so each adjacent angle is: $$180^\circ - 39^\circ = 141^\circ$$ 5. **Step 3: Understand the diagonals' effect** The diagonals bisect the angles and are perpendicular, so each angle at the intersection is 90°. 6. **Step 4: Find the numbered angles inside the rhombus** - Angles 1 and 3 are half of the 39° angles because diagonals bisect the vertex angles: $$\text{Angle 1} = \text{Angle 3} = \frac{39^\circ}{2} = 19.5^\circ$$ - Angles 2 and 4 are half of the 141° angles: $$\text{Angle 2} = \text{Angle 4} = \frac{141^\circ}{2} = 70.5^\circ$$ 7. **Final answer:** - Angle 1 = 19.5° - Angle 2 = 70.5° - Angle 3 = 19.5° - Angle 4 = 70.5° These angles correspond to the four triangles formed by the diagonals inside the rhombus.