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.

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.