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To solve for \( a^\circ \) in the given triangle, we will use the fact that the sum of the interior angles in any triangle is always \( 180^\circ \).

The angles given in the triangle are:
- \( a^\circ \)
- \( 21^\circ \)
- \( (2a + 6)^\circ \)

Thus, we can set up the following equation:

\[
a + 21 + (2a + 6) = 180
\]

Now, let's solve this equation step by step.

\[
a + 21 + 2a + 6 = 180
\]
\[
3a + 27 = 180
\]
\[
3a = 180 - 27
\]
\[
3a = 153
\]
\[
a = \frac{153}{3} = 51
\]

However, there seems to be a slight discrepancy, as none of the answer choices match \( 51^\circ \). Since the diagram states "not to scale," it is possible that an error in interpretation occurred.

Could you confirm any additional information from the diagram or suggest how we should proceed further?

What is the value of a? The diagram is not to scale. The angles provided are 21°, (2a + 6)°, and a°.

Find the value of the angle 'a' in a triangle, given two other angles: 21° and (2a + 6)°. Using the angle sum theorem and algebra, solve this geometry problem with a step-by-step explanation. Suitable for Grades 8-10.

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