SOLUTION: △ D E F , m ∠ D = 2 x + 3 , m ∠ E = 5 x , a n d m ∠ F = 4 x + 1. find the measure of x m ∠ D m ∠ E m ∠ F

Algebra ->  Triangles -> SOLUTION: △ D E F , m ∠ D = 2 x + 3 , m ∠ E = 5 x , a n d m ∠ F = 4 x + 1. find the measure of x m ∠ D m ∠ E m ∠ F       Log On


   

Question 1170312: △ D E F , m ∠ D = 2 x + 3 , m ∠ E = 5 x , a n d m ∠ F = 4 x + 1.

find the measure of
x
m ∠ D
m ∠ E
m ∠ F
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the angles is 180 degrees
2x+3+5x+4x+1=180
11x+4=180
11x=176
x=16 degrees
so
Angle D is 35 degrees
angle E is 80 degrees
angle F is 65 degrees

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

the sum of all angles in △ DEF+ is 180
if
m ∠ D+=+2x+%2B+3+,
+m+∠+E+=+5x , a n d
m+∠ F+=+4x+%2B+1
we have
2x+%2B+3%2B5x%2B4x+%2B+1=180......solve for x
11x+%2B+4=180
11x=180-4
11x=176
x=176%2F11
x=16

the measure of
m ∠ D+=+2%2A16+%2B+3+=>m ∠ D+=+35+
+m+∠+E+=+5%2A16=>+m+∠+E+=+80
m+∠ F+=+4%2A16+%2B+1=>m+∠ F+=+65