In the given triangle $PQR$, it is mentioned that $PQ = PR$, making it an isosceles triangle.

• Since $PQ = PR$, the angles opposite these sides, which are $\angle PQR$ and $\angle PRQ$, are equal.
• The angle at $Q$ is given as $2a^\circ$, so $\angle PQR = 2a^\circ$.
• Let $\angle PRQ$ also be equal to $2a^\circ$ because of the isosceles property.

Now, using the angle sum property of a triangle:

$\angle P + \angle PQR + \angle PRQ = 180^\circ$

Substituting the known angles:

$a^\circ + 2a^\circ + 2a^\circ = 180^\circ$

Simplifying:

$5a^\circ = 180^\circ$

$a = \frac{180^\circ}{5} = 36^\circ$

So, the value of $a$ is 36 degrees.

Would you like further details or have any questions?

Here are 5 related questions you might find useful:

1. What are the properties of an isosceles triangle?
2. How can we prove the angle sum property of a triangle geometrically?
3. What is the relationship between side lengths and angles in any triangle?
4. How would the calculation change if $PQ \neq PR$?
5. What is the sum of the exterior angles of any triangle?

Tip: In isosceles triangles, the two base angles are always equal, which simplifies many problems involving triangle properties.