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.
<pre>Let m&#8736E be x, and m&#8736F, y
Then m&#8736D = 2(x + y), or 2x + 2y
Since the angles of a triangle sum to 180<sup>o</sup>, then we get:
&#8736D + &#8736E + &#8736F = 180
2x + 2y + x + y = 180
3x + 3y = 180
3(x + y) = 3(60) ------ Factoring out GCF, 3
x + y = 60
Since &#8736E = x, and &#8736F = y, then &#8736s E and F sum to 60<sup>o</sup>.
Therefore, &#8736D MUST be 120<sup>o</sup> (180 - 60), which makes the triangle OBTUSE (CHOICE D).