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

CDEis an equilateral triangle.

CDEis an isosceles triangle.

n= 60 degrees

n= 90 degrees

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- Jun 21st 2007, 05:42 PM #1

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## 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

- Jun 21st 2007, 06:44 PM #2

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- Jun 21st 2007, 07:27 PM #3
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 $\displaystyle 60^{ \circ}$