In the image provided, the question asks to find the measures of two angles $m \angle BAC$ and $m \angle CAD$, using the given expressions:

• $m \angle BAC = (15x - 2)^\circ$
• $m \angle CAD = (7x + 4)^\circ$

Since $\angle BAC$ and $\angle CAD$ are adjacent angles and form a straight line at point $A$, the sum of these angles should be $180^\circ$. This gives the equation:

$(15x - 2) + (7x + 4) = 180$

Let's solve this equation step by step.

1. Combine like terms: $15x + 7x - 2 + 4 = 180$ $22x + 2 = 180$

2. Subtract 2 from both sides: $22x = 178$

3. Divide both sides by 22: $x = \frac{178}{22} = 8.09$

Now that we have the value of $x$, substitute it back into the expressions for $m \angle BAC$ and $m \angle CAD$.

1. $m \angle BAC = 15x - 2 = 15(8.09) - 2 = 121.35 - 2 = 119.35^\circ$
2. $m \angle CAD = 7x + 4 = 7(8.09) + 4 = 56.63 + 4 = 60.63^\circ$

So, the measures of the angles are approximately:

• $m \angle BAC \approx 119.35^\circ$
• $m \angle CAD \approx 60.63^\circ$

Let me know if you'd like further clarification on the steps or additional details.

Here are 5 related questions to explore:

1. What is the sum of the interior angles in a triangle?
2. How do you find the measure of an exterior angle of a triangle?
3. How do adjacent angles relate to each other in terms of their sum?
4. What are supplementary and complementary angles?
5. How can you solve equations with variables on both sides?

Tip: When solving for angles on a straight line, always remember that their sum must equal 180°.