The diagram shows a rhombus, as indicated by the equal lengths of all four sides, and it has a diagonal that divides one of the angles into two equal parts. Here’s how to find the values of $a$ and $b$:

1. Angle $a$: Since the diagonal bisects the angle of the rhombus into two equal parts, we know that: $2a = 52^\circ$ Dividing both sides by 2, we get: $a = 26^\circ$

2. Angle $b$: Opposite angles in a rhombus are equal, and the two angles adjacent to $a$ are supplementary to it (they sum to $180^\circ$). So: $b = 180^\circ - 52^\circ = 128^\circ$

Final Answer:

• $a = 26^\circ$
• $b = 128^\circ$

Would you like more details or have questions?

Here are five related questions to expand your understanding:

1. What properties define a rhombus, and how do they apply to angle calculations?
2. How would the angle values change if the given angle was different?
3. Can the diagonal of a rhombus ever be an angle bisector if it’s not a line of symmetry?
4. What is the difference between a rhombus and a kite in terms of angles and diagonals?
5. How do you calculate the area of a rhombus if you know its diagonals?

Tip: In any rhombus, diagonals bisect each other at right angles, helping to form two congruent triangles.