In the triangle MNE, the height NC is also the bisector of the angle MNE. Find the angle E and angle N if M = 35.

Given:
Triangle MNE
Height and bisector of angle MNE – NC
Angle M = 35.
To find:
Angle E and N.

Decision:
Consider a triangle MNC. NMC angle is given. The angle MCN = 90 degrees as it is the height.
1) angle MNC = 180 – (angle M + angle C) =
180 – (35 + 90) = 55 – in each triangle, the sum of 3 angles is 180.
2) Angle MNC = angle CNE, since NC is also a bisector by condition.
MNE angle = MNC angle + CNE angle =
55 + 55 = 110
3) Angle NEM = 180 – (EMN + MNE) =
180 – (35 + 110) = 35
Answer: 110 and 35.