We are given two expressions for angles in terms of $x$:

1. $13x - 48^\circ$
2. $7x + 36^\circ$

If these two angles form a specific relationship, such as being supplementary (sum to $180^\circ$) or complementary (sum to $90^\circ$), we could set up an equation to solve for $x$. I will assume that they are supplementary angles (sum to $180^\circ$).

Step 1: Set up the equation

Since the two angles are supplementary, we can write: $(13x - 48^\circ) + (7x + 36^\circ) = 180^\circ$

Step 2: Combine like terms

Simplify the left-hand side of the equation: $13x - 48 + 7x + 36 = 180$ $(13x + 7x) + (-48 + 36) = 180$ $20x - 12 = 180$

Step 3: Solve for $x$

First, add $12$ to both sides: $20x = 192$ Now, divide both sides by $20$: $x = \frac{192}{20} = 9.6$

Step 4: Find the measure of each angle

Now that we know $x = 9.6$, substitute this value back into each angle expression:

1. $13x - 48^\circ$: $13(9.6) - 48 = 124.8^\circ - 48 = 76.8^\circ$

2. $7x + 36^\circ$: $7(9.6) + 36 = 67.2^\circ + 36 = 103.2^\circ$

Final Answer:

• The first angle is $76.8^\circ$.
• The second angle is $103.2^\circ$.

These two angles sum to $180^\circ$, confirming they are supplementary.

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Do you want more details on any of the steps?

Here are 5 related questions:

1. How do we solve equations involving multiple variables?
2. Can angles ever have negative measures? When might this happen?
3. What is the difference between supplementary and complementary angles?
4. How can we verify our answers when solving for unknowns?
5. How would the process change if the angles were complementary instead?

Tip: When solving equations, always double-check your simplifications of terms to avoid minor mistakes!