HELP! Geometry Test

Question

Help! T is in the interior of ∠ROS. S is in the interior or ∠TOP. m∠ROP = 160°, m∠TOP =100 °, and m∠TOS = m∠SOP

FIND:

a) m∠SOP =

b) m∠ROS =

Answer 1

m<ROT + m<TOS+ m<SOP = 160°

m<TOP = 100°

As m<TOS + m<SOP = m<TOP and m<TOS = m<SOP,

a)2m<SOP = m<TOP = 100°, so m<SOP = 50°

b) m<ROS + m<SOP = m<SOP = 160°, so m<ROS = 160° - 50°= 110°