# Thread: what is necessary for m to be 60?

1. ## what is necessary for m to be 60?

In the figure below, ABC is an equilateral triangle. In order to have m = 60 degrees, which condition is necessary? think it is n=60 or

CDE is an equilateral triangle.
CDE is an isosceles triangle.
n = 60 degrees
n = 90 degrees

2. The picture is not working.
As well in your other posts.

3. Originally Posted by sanee66
In the figure below, ABC is an equilateral triangle. In order to have m = 60 degrees, which condition is necessary? think it is n=60 or

CDE is an equilateral triangle.
CDE is an isosceles triangle.
n = 60 degrees
n = 90 degrees
Here's the first problem

Note that $\displaystyle \angle ACB \mbox { , } \angle m \mbox { and } \angle n$ are supplementary (they add up to $\displaystyle 180^{ \circ}$), since they are angles on a straight line.

Since $\displaystyle \triangle ABC$ is equilateral, $\displaystyle \angle ACB = 60^{ \circ}$

So we have $\displaystyle 60 + m + n = 180$

$\displaystyle \Rightarrow n = 180 - 60 - m$

We want $\displaystyle m$ to be $\displaystyle 60^{ \circ}$ so plug that in

$\displaystyle \Rightarrow n = 180 - 60 - 60 = 60$

So $\displaystyle n$ must be $\displaystyle 60^{ \circ}$