SOLUTION: In triangle DEF: if m < D = 2 (m < E + m < F) which term best describes triangle DEF? A) Acute B) Equiangular C) Right D) Obtuse An explanation would be nice, thank you.

Algebra ->  Triangles -> SOLUTION: In triangle DEF: if m < D = 2 (m < E + m < F) which term best describes triangle DEF? A) Acute B) Equiangular C) Right D) Obtuse An explanation would be nice, thank you.      Log On


   

Question 1076771: In triangle DEF:
if m < D = 2 (m < E + m < F) which term best describes triangle DEF?
A) Acute
B) Equiangular
C) Right
D) Obtuse
An explanation would be nice, thank you.
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
by definition, the sum of all interior angles in triangle is 180
if m < D+= 2 (m < E + m <+F), could be true only if
for example m < D=120+ and m < E=34 + m <+F=26
D+=2%28E%2BF%29
120=2%2834%2B26%29
120=2%2860%29
120=120
the term that best describes triangle DEF is C) obtus
ps: sorry for previous mistake

Answer by MathTherapy(10810) About Me  (Show Source):
You can put this solution on YOUR website!
In triangle DEF:
if m < D = 2 (m < E + m < F) which term best describes triangle DEF?
A) Acute
B) Equiangular
C) Right
D) Obtuse
An explanation would be nice, thank you.
Let m∠E be x, and m∠F, y

Then m∠D = 2(x + y), or 2x + 2y

Since the angles of a triangle sum to 180o, then we get:

∠D + ∠E + ∠F = 180

2x + 2y + x + y = 180

3x + 3y = 180

3(x + y) = 3(60) ------ Factoring out GCF, 3

x + y = 60

Since ∠E = x, and ∠F = y, then ∠s E and F sum to 60o.

Therefore, ∠D MUST be 120o (180 - 60), which makes the triangle OBTUSE (CHOICE D).