In the image, we have two angles represented by the expressions $3x + 20$ and $2x - 10$, which appear to form a linear pair (angles that are adjacent and sum up to 180°). This means that:

$(3x + 20) + (2x - 10) = 180$

Now, let's solve for $x$:

1. Combine like terms: $3x + 20 + 2x - 10 = 180$ $5x + 10 = 180$

2. Subtract 10 from both sides: $5x = 170$

3. Divide both sides by 5: $x = 34$

Thus, $x = 34$.

Verifying the Angles:

Now substitute $x = 34$ back into the expressions for the angles:

• $3x + 20 = 3(34) + 20 = 102 + 20 = 122^\circ$
• $2x - 10 = 2(34) - 10 = 68 - 10 = 58^\circ$

The sum is: $122^\circ + 58^\circ = 180^\circ$

Thus, the solution is correct.

Would you like further details or clarifications?

Relative Questions:

1. How do you identify a linear pair of angles?
2. Can angles on a straight line ever sum to more or less than 180°?
3. What happens if $x$ results in a negative angle?
4. What other relationships between angles can help solve such problems?
5. How can you verify if angles are supplementary or complementary?

Tip:

Always remember that angles forming a straight line (linear pair) will sum to 180°, which is a useful property in many geometric problems.