# what is necessary for m to be 60?

• Jun 21st 2007, 05:42 PM
sanee66
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 https://www.d2l.mvps.mde.k12.ms.us/c.../quiz5b_q5.gif

CDE is an equilateral triangle.
CDE is an isosceles triangle.
n = 60 degrees
n = 90 degrees
• Jun 21st 2007, 06:44 PM
ThePerfectHacker
The picture is not working.
As well in your other posts.
• Jun 21st 2007, 07:27 PM
Jhevon
Quote:

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 https://www.d2l.mvps.mde.k12.ms.us/c.../quiz5b_q5.gif

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}\$