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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.

In the triangle below, PQ = PR. Calculate the value of a.

In this problem, we calculate the value of 'a' in an isosceles triangle where PQ = PR and ∠PQR = 2a°. Using the angle sum property of triangles and isosceles triangle properties, the value of a is determined. Suitable for students in Grades 8-10.

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