What is the proof of the following?

Question

Given: m∠LAE = 8x + 9, m∠EAN = 4x + 11, m∠LAN = 16x

Prove: x = 5

Answer 1

It is likely even without a diagram, that this problem is requiring the use of the angle addition postulate. I am guessing you have adjacent angles with "A" the common vertex and that ray AE is in the interior of ∠LAN.

If that is the case, then by the angle addition postulate m∠LAE + m∠EAN = m∠LAN. Substituting the algebraic expressions that represent the measures of those angles (given) you have:

8x+9 + 4x+11 = 16x.

Solve that equation for x using properties like addition property for equality, division property for equality, etc. and hope that you end up with x= 5 (Q.E.D).