https://file.aiquickdraw.com/mathbot/file/1730147353163j6h2k60d.jpg

Let’s analyze the problem.

We have two parallel lines \(c\) and \(d\) cut by two transversals \(a\) and \(b\). In the diagram:
- \( \angle BAC = (2x + 21)^\circ \) 
- \( \angle ABC = 5x^\circ \)  

### Step-by-Step Solution:

Since the two lines \(c\) and \(d\) are parallel, and angles \( \angle BAC \) and \( \angle ABC \) lie within the same triangle \( \triangle ACB \), we can apply the **triangle angle sum property**. The sum of the interior angles of a triangle is always \(180^\circ\).

\[
\angle BAC + \angle ABC + \angle ACB = 180^\circ
\]

Substitute the given angle measures:

\[
(2x + 21)^\circ + 5x^\circ + \angle ACB = 180^\circ
\]

Simplify:

\[
7x + 21 + \angle ACB = 180^\circ
\]

\[
\angle ACB = 180^\circ - 7x - 21
\]

\[
\angle ACB = 159^\circ - 7x
\]

Now, you’ll need either a value for \(x\) or more information to solve for the numerical value of \( \angle ACB \). If there’s additional information, please share it.

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Do you have any questions or would you like to proceed with further steps?  

Here are 5 related questions to consider:
1. How can we solve for \(x\) if given another angle value in the triangle?
2. What are the properties of parallel lines and transversals used here?
3. How does the triangle angle sum theorem apply to non-right triangles?
4. Can you calculate exterior angles using these values?
5. How do you determine if two lines are parallel based on angle relationships?

**Tip:** When working with parallel lines and transversals, look for corresponding or alternate interior angles—they are often equal.

Mr. Haynes posted his assignment on the board. What is the value of ∠ACB?

Find the value of ∠ACB in a triangle intersected by two parallel lines and transversals, using the triangle angle sum theorem. This geometry problem is ideal for students in Grades 8-10 and covers key concepts such as parallel lines, angle relationships, and the triangle angle sum property.

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