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The problem asks to find \( x \) using the given angles:

- \( m \angle BJK = 146 + 2x \),
- \( m \angle IJK = 172^\circ \),
- \( m \angle IJB = 2x + 26 \).

From the diagram, we can see that:

\[
m \angle IJK = m \angle BJK + m \angle IJB
\]

This means that the sum of \( m \angle BJK \) and \( m \angle IJB \) should equal \( m \angle IJK \), which is \( 172^\circ \).

Let's set up the equation:

\[
(146 + 2x) + (2x + 26) = 172
\]

Now, we can solve for \( x \).

First, simplify the left-hand side:

\[
146 + 2x + 2x + 26 = 172
\]
\[
172 + 4x = 172
\]

Next, subtract 172 from both sides:

\[
4x = 0
\]

Divide by 4:

\[
x = 0
\]

Thus, \( x = 0 \).

Would you like a more detailed explanation or any further clarifications?

Here are 5 related questions for further practice:

1. What is the value of \( m \angle BJK \) when \( x = 0 \)?
2. What is the value of \( m \angle IJB \) when \( x = 0 \)?
3. If \( m \angle IJK = 180^\circ \), how would this affect the value of \( x \)?
4. What geometric property do the angles \( m \angle BJK \) and \( m \angle IJB \) share?
5. How would the problem change if \( m \angle IJK = 150^\circ \)?

**Tip**: Always remember that the sum of angles in a triangle is 180° and that the exterior angle is equal to the sum of the two non-adjacent interior angles.

Find x if m∠BJK = 146 + 2x, m∠IJK = 172°, and m∠IJB = 2x + 26.

Discover how to find x using the sum of angles and exterior angle properties in a geometry problem. This guide offers a clear, step-by-step solution to understanding angle calculations in triangles.

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