https://file.aiquickdraw.com/mathbot/file/17266121275444joa5lij.jpg

In the provided image, we are asked to find the measure of \( \angle MRK \) given that \( \angle MRJ = 116^\circ \).

### Step-by-Step Solution:
- From the diagram, angles \( \angle MRJ \) and \( \angle MRK \) are **linear pairs** because they share the same vertex \( R \) and are adjacent to each other along the line \( JK \).
- Linear pairs of angles are **supplementary**, meaning their sum is \( 180^\circ \).

### Calculation:
- We are given that \( \angle MRJ = 116^\circ \).
- To find \( \angle MRK \), we subtract the given angle from \( 180^\circ \):

\[
\angle MRK = 180^\circ - 116^\circ = 64^\circ
\]

Thus, \( \angle MRK = 64^\circ \).

### Final Answer:
\( m\angle MRK = 64^\circ \)

Let me know if you need further details or have any questions!

Here are 5 related questions to expand your understanding:
1. What is the sum of all interior angles in a triangle?
2. How are vertically opposite angles related in such diagrams?
3. Can angles formed by intersecting lines ever be complementary? Why?
4. What are alternate interior angles and how do they relate to parallel lines?
5. If two lines are perpendicular, what is the relationship between their adjacent angles?

**Tip**: When dealing with angles formed by intersecting lines, always check for supplementary and vertically opposite angle pairs to simplify the problem!

If m∠MRJ = 116°, then what is m∠MRK?

This problem involves finding the measure of ∠MRK when m∠MRJ is given as 116°. Key concepts include linear pairs and supplementary angles. A step-by-step solution is provided for students in Grades 7-9.

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