https://file.aiquickdraw.com/mathbot/file/1726854484787hdxs1oi0.jpg

In this image, you are asked to find the measure of each angle. We are given two expressions for the angles: 

- \((5x - 10)^\circ\)
- \((7x + 4)^\circ\)

The key fact to use here is that these two angles form a right angle at point \(A\), meaning their sum is \(90^\circ\).

So, we can set up the equation:

\[
(5x - 10) + (7x + 4) = 90
\]

Let me solve this equation for \(x\):

\[
5x - 10 + 7x + 4 = 90
\]
\[
12x - 6 = 90
\]
\[
12x = 96
\]
\[
x = 8
\]

Now that we know \(x = 8\), we can find the measure of each angle:

1. The first angle is \((5x - 10)\):
   \[
   5(8) - 10 = 40 - 10 = 30^\circ
   \]

2. The second angle is \((7x + 4)\):
   \[
   7(8) + 4 = 56 + 4 = 60^\circ
   \]

So, the two angles are:

- \( \angle BAC = 30^\circ \)
- \( \angle CAD = 60^\circ \)

Let me know if you'd like more details or have any further questions!

### Here are five related questions:
1. What are complementary angles?
2. How do you find the value of \(x\) when two angles are supplementary?
3. Can angles be expressed in radians as well as degrees?
4. How do you solve for \(x\) when three angles sum to 180°?
5. How would the solution change if the angles were supplementary instead of complementary?

### Tip:
Always check if angles form a right angle, straight angle, or other recognizable patterns, as these can provide useful relationships for solving problems.

Find the measure of each angle given the expressions (5x - 10)° and (7x + 4)°, knowing that they form a right angle at point A.

Learn how to find the measures of two complementary angles given by the expressions (5x - 10)° and (7x + 4)°. This step-by-step solution covers algebraic equations and complementary angle theorems, suitable for Grades 7-9.

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