w lies in the interior of angle xyz. angle xyw is equal to 7x-2. angle wyz is equal to 2x+15 angle xyz 139. find X

We are given that \( w \) lies in the interior of angle \( \angle XYZ \), meaning that:

\[
\angle XYZ = \angle XYW + \angle WYZ
\]

We know:

\[
\angle XYZ = 139^\circ
\]
\[
\angle XYW = 7x - 2
\]
\[
\angle WYZ = 2x + 15
\]

Now, using the fact that \( \angle XYZ = \angle XYW + \angle WYZ \), we can set up the equation:

\[
139 = (7x - 2) + (2x + 15)
\]

Simplifying the equation:

\[
139 = 7x - 2 + 2x + 15
\]
\[
139 = 9x + 13
\]

Now, subtract 13 from both sides:

\[
139 - 13 = 9x
\]
\[
126 = 9x
\]

Now, divide both sides by 9:

\[
x = \frac{126}{9}
\]
\[
x = 14
\]

Thus, \( x = 14 \).

### Would you like further clarification or details?

Here are 5 related questions to expand on this concept:
1. How would you find the value of \( \angle XYW \) and \( \angle WYZ \) using \( x = 14 \)?
2. What happens if point \( w \) lies on the angle bisector of \( \angle XYZ \)?
3. Can you use this method to solve for angles in non-linear figures?
4. How do complementary and supplementary angles relate to problems like this?
5. What would the solution be if \( \angle XYZ \) was a right angle?

**Tip:** Always double-check your equation setup, ensuring all angle relationships are properly accounted for.

w lies in the interior of angle xyz. angle xyw is equal to 7x-2. angle wyz is equal to 2x+15. angle xyz is 139°. find x.

Learn how to solve for x in the angle XYZ problem, where angles XYW and WYZ are given as algebraic expressions. This step-by-step solution uses the angle addition postulate and basic algebra, making it ideal for students in Grades 7-9.

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