Angle Kjr 015Bd3

1. **State the problem:** We are given that $m\angle MON=74^\circ$ and need to find $m\angle KJR$ using the diagram. 2. **Analyze the diagram and angles:** The two diagonal lines intersect at point $O$, creating vertical angles. Vertical angles are equal. 3. **Identify vertical angles:** $\angle MON$ and $\angle JOR$ are vertical angles, so $$m\angle MON = m\angle JOR = 74^\circ.$$ 4. **Look at the horizontal line through $K$, $O$, and $P$:** This line forms a straight angle of $180^\circ$ at $O$. Since $\angle JOR$ is $74^\circ$, the adjacent angle $\angle KOR$ satisfies $$m\angle KOR = 180^\circ - 74^\circ = 106^\circ.$$ 5. **Consider the triangle $KJR$:** Points $K$, $J$, and $R$ form a triangle. The angle $\angle KJR$ is at point $J$ between rays $JK$ and $JR$. 6. **Use the property of alternate interior angles or corresponding angles:** Since $JK$ and $KO$ are on the same line and $OR$ extends from $O$ to $R$, $\angle KJR$ corresponds to $\angle KOR$. 7. **Therefore, $m\angle KJR = m\angle KOR = 106^\circ$.** **Final answer:** $$m\angle KJR = 106^\circ.$$