Question

Find the degree measure of each angle in the triangle.

Answer 1

So, sides NL and NM are the same length, which means that this is an isosceles triangle. What do you know about angles in an isosceles triangle?

Answer 2

Doesn't the sum of the angles have to equal 180 degrees?

Answer 3

Yes!
That's true for all triangles.

Answer 4

Something else special about isosceles triangles (Where two sides are equal) is that the angles opposite the equal sides are also equal.

Answer 5

In your triangle, this means that angles L & M are equal. Since we know this, we can say:
\[\angle L = \angle M \\ 4x+22° = 3x+30°\]

Answer 6

If you solve for x, you can find angles L and M.

Once you have that, you can find angle N because you know they all have to add up to 180°.

Answer 7

How do you solve for x though?

Answer 8

You know that:
4x + 22 = 3x + 30.

Start by isolating the variable.

Answer 9

alright i figured that one out but now Im stuck on this one

Answer 10

You know that angle E equals angle D, and that all of the angles add up to 180 degrees.

\[\angle C + \angle D + \angle E = 180° \\ \angle C + \angle E + \angle E = 180° \\ 4x + (5x-8) + (5x-8) = 180°\]

Answer 11

did you get x=14 ?