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.

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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)   (Show Source): You can put this solution on YOUR website!
by definition, the sum of all interior angles in triangle is
if < = ( < + <), could be true only if
for example < and < + <




the term that best describes triangle is C)
ps: sorry for previous mistake
Answer by MathTherapy(10810)   (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). 

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