https://file.aiquickdraw.com/mathbot/file/1729549078720yexogah1.jpg

The problem involves a set of angles, and we're tasked with solving for \( k \). 

From the diagram:

- There is a right angle between the two intersecting lines, indicated by a 90-degree angle.
- One angle is labeled \( (k+2)^\circ \).
- Another angle is labeled \( (2k - 2)^\circ \).

### Key concept:
The angles around the point where the lines intersect must sum to \( 180^\circ \) because the total measure around a point is always \( 180^\circ \).

Thus, we can set up the following equation:

\[
(k + 2)^\circ + (2k - 2)^\circ + 90^\circ = 180^\circ
\]

### Let's solve for \( k \):

1. Combine the like terms:
\[
(k + 2) + (2k - 2) + 90 = 180
\]
\[
3k + 90 = 180
\]

2. Subtract 90 from both sides:
\[
3k = 90
\]

3. Divide by 3:
\[
k = 30
\]

Thus, the value of \( k \) is \( 30 \).

Would you like further details or have any questions about this solution?

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Here are 5 related questions you can try:
1. If \( k = 30 \), what is the measure of the \( (k + 2)^\circ \) angle?
2. What would be the measure of the \( (2k - 2)^\circ \) angle when \( k = 30 \)?
3. How would the equation change if the right angle was altered to a different value?
4. Can you determine if the angles form a linear pair in this diagram?
5. How would the problem change if \( k \) were expressed as a fractional value?

**Tip:** Always remember that the sum of angles around a point on a straight line is 180 degrees, which is a key property when dealing with intersecting lines.

Solve for the value of k given the angles (k+2)°, (2k-2)°, and a 90° angle.

Learn how to solve for k in a geometric problem involving angles (k+2)°, (2k-2)°, and a right angle. This solution uses the angle sum property and basic algebra. Suitable for students in Grades 8-10.

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