Some pls explain this to me ((number 5))

MP ⊥ LO ⇒ proved

Step-by-step 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