https://file.aiquickdraw.com/mathbot/file/1726373641207mc6m3x34.jpg

The problem asks to solve for \( t \) in an equation involving two angles: \( (6t + 6)^\circ \) and \( (7t - 7)^\circ \). These two angles appear to form a linear pair, meaning their sum equals 180° because they are adjacent and form a straight line.

To solve for \( t \), we can use the equation:

\[
(6t + 6) + (7t - 7) = 180
\]

### Step-by-step solution:

1. Combine like terms:
\[
6t + 7t + 6 - 7 = 180
\]
\[
13t - 1 = 180
\]

2. Add 1 to both sides:
\[
13t = 181
\]

3. Divide both sides by 13:
\[
t = \frac{181}{13} = 13.92
\]

However, based on the answer shown in your image, it seems that \( t = 13 \) was used. This could suggest rounding was applied in the solution process, though it's more typical to use the exact value. 

Would you like any further details or clarifications?

Here are some related questions you can explore:
1. What are adjacent angles and how do they relate to a linear pair?
2. How do you solve linear equations like the one shown here?
3. What happens when the angles in a triangle are set equal to specific values?
4. How are angle pair relationships important in geometry?
5. How can rounding impact the final answer in solving equations?

**Tip:** Always check if a rounding approximation is needed or if an exact value is expected for a precise solution!

Solve for the value of t based on the given angles: (6t + 6)° and (7t - 7)°, which form a linear pair.

Learn how to solve for t in a linear pair equation where two angles, (6t + 6)° and (7t - 7)°, sum to 180°. This step-by-step explanation covers core algebraic concepts, such as solving linear equations and the linear pair theorem. Ideal for students in Grades 8-10.

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