The image shows two angles, one given as $52^\circ$ and the other as $4x - 8$. The two angles are supplementary, meaning they add up to $180^\circ$ because they form a straight line. Here's how we solve for $x$ and the missing angle:

Step 1: Set up the equation for supplementary angles

$52 + (4x - 8) = 180$

Step 2: Simplify and solve for $x$

$52 + 4x - 8 = 180$ $44 + 4x = 180$ $4x = 180 - 44$ $4x = 136$ $x = \frac{136}{4} = 34$

So, $x = 34$.

Step 3: Solve for the missing angle

The missing angle is $4x - 8$. Now that we know $x = 34$, substitute this value into the expression: $4(34) - 8 = 136 - 8 = 128^\circ$

Final Answers:

• $x = 34$
• Missing angle = $128^\circ$

Let me know if you'd like further details! Here are 5 related questions for practice:

1. What would the missing angle be if the given angle was $60^\circ$ instead of $52^\circ$?
2. If the equation was $3x + 10$ instead of $4x - 8$, how would the solution change?
3. How do you know that the angles are supplementary in this problem?
4. What are complementary angles, and how are they different from supplementary angles?
5. What if the angles were complementary instead? How would you set up the equation?

Tip: Always check the angle relationship (complementary or supplementary) before solving for $x$ in geometric problems!