https://file.aiquickdraw.com/mathbot/file/172881505746257qrh00l.jpg

The image shows a problem where we are asked to find the value of \( a \) based on the angles presented in the figure. The angles are labeled as:

- \( (a + 10)^\circ \)
- \( (3a - 80)^\circ \)
- The middle angle as \( a^\circ \).

These angles are vertically opposite angles, which means that:

\[
(a + 10)^\circ + (3a - 80)^\circ = a^\circ
\]

This is because the sum of angles on a straight line equals \( 180^\circ \). Now, let's solve the equation:

\[
(a + 10) + (3a - 80) = 180
\]
\[
a + 10 + 3a - 80 = 180
\]
\[
4a - 70 = 180
\]
\[
4a = 250
\]
\[
a = \frac{250}{4} = 62.5
\]

So, the value of \( a \) is \( 62.5^\circ \).

Would you like further details or have any other questions?

Here are 5 related questions to expand on this:
1. What are vertically opposite angles?
2. How do we use the straight line property in angle calculations?
3. Can you calculate the other angles once \( a \) is known?
4. How do you solve equations involving angles in geometry?
5. What is the importance of identifying opposite and adjacent angles?

**Tip:** When solving angle problems, always look for properties such as vertically opposite angles, complementary angles, or the sum of angles on a straight line. These are key to forming equations.

What is the value of 'a' in the figure below?

Learn how to solve for the value of 'a' in an angle equation using vertically opposite angles and the sum of angles on a straight line. The problem involves basic algebraic equations and is suitable for students in Grades 9-10.

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