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.