The problem presented in the image asks to determine the measures of two complementary angles, $\angle 1$ and $\angle 2$.

Given:

• The angles $\angle 1$ and $\angle 2$ are complementary, meaning their sum is 90°.
• $m\angle 1 = (2x + 15)^\circ$
• $m\angle 2 = (4x - 3)^\circ$

To Find:

• The values of $\angle 1$ and $\angle 2$.

Solution:

Since the angles are complementary, their sum is: $m\angle 1 + m\angle 2 = 90^\circ$

Substituting the given expressions: $(2x + 15) + (4x - 3) = 90$

Combine like terms: $6x + 12 = 90$

Subtract 12 from both sides: $6x = 78$

Divide by 6: $x = 13$

Now, substitute $x = 13$ back into the expressions for $m\angle 1$ and $m\angle 2$:

$m\angle 1 = 2(13) + 15 = 26 + 15 = 41^\circ$ $m\angle 2 = 4(13) - 3 = 52 - 3 = 49^\circ$

Final Answer:

• $m\angle 1 = 41^\circ$
• $m\angle 2 = 49^\circ$

These measures confirm that $41^\circ + 49^\circ = 90^\circ$, so the solution is consistent.

Would you like further details or have any questions?

Here are 5 related questions:

1. What would happen if $\angle 1$ and $\angle 2$ were supplementary instead of complementary?
2. How would the equation change if one of the angles was expressed as $5x + 20$ instead?
3. What are vertical angles, and how do they differ from complementary angles?
4. How would you solve for $x$ if one angle was given in radians?
5. What is the relationship between the angles in a right triangle?

Tip: Remember that complementary angles always add up to 90°, and this concept is often useful in geometric proofs and problem-solving.