Question

Point A is the incenter of ΔDEF.

Point A is the incenter of triangle D E F. Lines are drawn from the points of the triangle to point A. Lines are drawn from point A to the sides of the triangle to form right angles and line segments A X, A Y, and A Z. Angle L D A is 27 degrees. Angle A D M is (3 n minus 6) degrees.
What is the value of n?

7
11
14
15

Answer 1

Since A is the incenter, DA bisects angle EDF, so ∠LDA = ∠ADM. Thus
27 = 3n − 6 → 3n = 33 → n = 11.

Answer: 11.