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

Answer:

The correct option is;

11

Step-by-step explanation:

The incenter is the point where the interior angle bisectors of the triangle meet, hence the interior angles are each bisected into two by the segments DA, EA, and FA respectively

Given that point A is the incenter of ΔDEF, we have;

∠FDE = ∠XDY is bisected by DA which gives ∠XDA = ∠YDA

∠LDA = ∠XDA = 27

∠MDA = ∠YDA = 3··n - 6

Therefore, 27 = 3·n - 6

3·n = 27 + 6 = 33

n = 33/3 = 11°