Answer:
MP ⊥ LO ⇒ proved
Explanation:
In the given figure
∵ m∠LPM = m∠MNO ⇒ given
∵ m∠MNO = m∠MPO ⇒ given
→ If the measure of an angle equals the measures of another two
angles, then the two angles must be equal in measures
∴ m∠LPM = m∠MPO ⇒ proved
∵ P ∈ line LO
∵ ∠ LPM and ∠MPO are adjacent angles
∴ ∠LPM and ∠MPO formed a pair of linear angles
→ The measure of the linear pair angles is 180°
∴ m∠LPM + m∠MPO = 180°
∵ m∠LPM = m∠MPO
→ That means the measure of each one is 180° divided by 2
∴ m∠LPM = m∠MPO = 180° ÷ 2
∴ m∠LPM = m∠MPO = 90°
∵ MP intersect LO at P and formed right angles at P
→ That means MP is perpendicular to LO
∴ MP ⊥ LO ⇒ proved