SOLUTION: If the measure of an exterior angle drawn at vertex M of triangle LMN is x, then m L + m N is what? (sorry I don't have the angle symbol)

Algebra ->  Triangles -> SOLUTION: If the measure of an exterior angle drawn at vertex M of triangle LMN is x, then m L + m N is what? (sorry I don't have the angle symbol)       Log On


   

Question 107832: If the measure of an exterior angle drawn at vertex M of triangle LMN is x, then m L + m N is what? (sorry I don't have the angle symbol)

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
If I understand your question correctly, then the answer is that x equals mL + mN.
.
Look at it this way: angle M and its exterior angle are formed by a straight line. Therefore, the
measure of angle M plus the measure of its supplementary angle can be written as:
.
mM + x = 180 degrees
.
subtracting mM from both sides of this equation results in:
.
x = 180 - mM <=== remember this equation
.
and for the interior angles of this triangle mM + mL + mN = 180 degrees
.
subtracting mM from both sides of this equation results in the equation becoming:
.
mL + mN = 180 - mM <=== remember this equation also
.
Now look at the two equations we have derived. The right sides of these two equations
are the same ... and therefore, they are equal. This means that the left sides must be
equal also. In one of the equations the left side is x. And in the other equation the
left side is mL + mN. So we can write:
.
x = mL + mN
.
And this is what was stated at the beginning ... the measure of the exterior angle x
is equal to the two interior angles on the opposite side of the triangle.
.
Hope this clarifies it for you.
.