1. **Stating the problem:** We are given multiple angles formed by intersecting lines and need to find the missing angle(s) based on the given angle measures. 2. **Important rules:** - Vertical angles are equal. - Angles on a straight line sum to 180°. - Angles around a point sum to 360°. 3. **Given angles:** $$m\angle 1 = 70^\circ, m\angle 5 = 64^\circ, m\angle 14 = 131^\circ, m\angle 22 = 63^\circ, m\angle 27 = 58^\circ, m\angle 48 = 38^\circ, m\angle 74 = 58^\circ, m\angle 86 = 129^\circ$$ 4. **Finding missing angles:** - Since vertical angles are equal, angles opposite each other at intersections are equal. - For example, if $m\angle 1 = 70^\circ$, then the vertical angle opposite to it is also $70^\circ$. - Angles on a straight line sum to 180°, so if one angle is $70^\circ$, the adjacent angle on the line is $180^\circ - 70^\circ = 110^\circ$. 5. **Example calculation:** - Using $m\angle 1 = 70^\circ$, the adjacent angle on the straight line is: $$180^\circ - 70^\circ = 110^\circ$$ - Using $m\angle 5 = 64^\circ$, the vertical angle opposite is also $64^\circ$. - Using $m\angle 14 = 131^\circ$, the adjacent angle on the straight line is: $$180^\circ - 131^\circ = 49^\circ$$ 6. **Summary:** - Each missing angle can be found by applying vertical angle equality or subtracting from 180° for adjacent angles on a straight line. - Without a specific missing angle requested, this method applies to all missing angles in the figure. **Final answer:** Use vertical angle equality and linear pair sum to 180° to find any missing angle based on the given angles.