The given diagram shows an angle $\angle ABC$ that is split into two angles by point $D$. The two angles formed are labeled as:

• $\angle ABD = (3x + 15)^\circ$
• $\angle DBC = (x + 7)^\circ$

The total angle $\angle ABC$ is given as $94^\circ$.

To find $x$, we can use the fact that:

$\angle ABC = \angle ABD + \angle DBC$

Substitute the given expressions:

$94^\circ = (3x + 15)^\circ + (x + 7)^\circ$

Now, simplify the equation:

$94 = 3x + 15 + x + 7$ $94 = 4x + 22$

Next, solve for $x$:

$94 - 22 = 4x$ $72 = 4x$ $x = \frac{72}{4} = 18$

Thus, the value of $x$ is $18$.

Would you like a detailed explanation on how I arrived at this solution? Let me know if you have further questions!

Here are some related questions you might want to explore:

1. How would the answer change if $m\angle ABC$ were different?
2. What is the measure of $\angle ABD$ and $\angle DBC$ using the value of $x$?
3. How do you verify that $\angle ABC$ sums up correctly with the found value of $x$?
4. What if another point $E$ divided $\angle ABC$ into three angles? How would you solve it?
5. Can you derive a similar equation for $x$ using a different geometric property?

Tip: Always check the sum of angles when solving for unknowns in angle-based geometry problems to ensure the relationships hold.