https://file.aiquickdraw.com/mathbot/file/17266014725403bb4cjna.jpg

The diagram you provided shows an angle situation where two angles are formed at point \( C \): 

1. One angle is given as \( (10x + 5)^\circ \).
2. Another angle is given as \( 75^\circ \).

Since point \( C \) is where two straight lines intersect, these two angles are supplementary, meaning they must add up to 180° because they form a straight line (line \( BD \)).

We can now set up the equation:

\[
(10x + 5) + 75 = 180
\]

Simplifying this equation:

\[
10x + 5 + 75 = 180
\]
\[
10x + 80 = 180
\]

Now, subtract 80 from both sides:

\[
10x = 100
\]

Finally, divide both sides by 10:

\[
x = 10
\]

So, the correct equation to solve for \( x \) is \( 10x + 80 = 180 \), which is one of the options provided in the image.

Would you like further details on the solution, or any other related question? Here are 5 follow-up questions you might be interested in:

1. What does it mean for two angles to be supplementary?
2. How do you solve linear equations like \( 10x + 80 = 180 \)?
3. What happens if two angles add up to less or more than 180°?
4. How do we classify angles based on their measures?
5. What is the significance of angles on a straight line?

**Tip**: Always check if two angles form a straight line when solving for supplementary angles; their sum should be 180°.

Which equation can be used to solve for x, given that two angles, (10x + 5)° and 75°, are supplementary and form a straight line?

Learn how to solve for x when two angles, (10x + 5)° and 75°, are supplementary and form a straight line. This algebraic solution helps students understand key geometry concepts like supplementary angles and basic algebra. Suitable for students in Grades 6-8.

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