In the image, the problem is asking for the measures of two angles, represented algebraically as:

• The larger angle is given by the expression $(21x + 19)^\circ$
• The smaller angle is given by the expression $(14x + 4)^\circ$

The two angles appear to be linear pair angles, meaning they are adjacent and their measures add up to $180^\circ$ since a linear pair always forms a straight line.

Let's solve for $x$:

1. The sum of the two angles must be $180^\circ$. So, we can set up the equation: $(21x + 19) + (14x + 4) = 180$

2. Combine like terms: $21x + 14x + 19 + 4 = 180$ $35x + 23 = 180$

3. Subtract 23 from both sides: $35x = 157$

4. Divide by 35: $x = \frac{157}{35} \approx 4.49$

Now, substitute $x$ back into the expressions for the angles:

• Larger angle: $21x + 19 = 21(4.49) + 19 = 94.29 + 19 = 113.29^\circ$

• Smaller angle: $14x + 4 = 14(4.49) + 4 = 62.86 + 4 = 66.86^\circ$

Conclusion:

• The larger angle measures approximately 113.29°.
• The smaller angle measures approximately 66.86°.

Would you like a more detailed explanation, or do you have any further questions?

Here are 5 related questions you can explore:

1. What are complementary and supplementary angles?
2. How do we solve systems of linear equations in geometry?
3. How can we verify the solution by checking the sum of the angles?
4. What is the relationship between adjacent angles in polygons?
5. How can we solve angle problems involving more complex expressions?

Tip: When working with linear pairs, always remember that their sum will be 180°, as they form a straight line.