Question
Triangle LMN is isoscele with Angle M ~ Angle L = 36 What are the Measures of Angle M and N?
Answers
GPT-4o mini
In an isosceles triangle, two sides are equal in length, which means the angles opposite those sides are also equal. In triangle LMN, you have angles M and L both equal to 36 degrees.
To find the measure of angle N, you can use the fact that the sum of all angles in a triangle is always 180 degrees:
\[
\text{Angle M} + \text{Angle L} + \text{Angle N} = 180^\circ
\]
Substituting the known values:
\[
36^\circ + 36^\circ + \text{Angle N} = 180^\circ
\]
Combining the angles:
\[
72^\circ + \text{Angle N} = 180^\circ
\]
Now, subtract 72 degrees from both sides:
\[
\text{Angle N} = 180^\circ - 72^\circ
\]
\[
\text{Angle N} = 108^\circ
\]
So, the measures of the angles are:
- Angle M = 36 degrees
- Angle L = 36 degrees
- Angle N = 108 degrees
To find the measure of angle N, you can use the fact that the sum of all angles in a triangle is always 180 degrees:
\[
\text{Angle M} + \text{Angle L} + \text{Angle N} = 180^\circ
\]
Substituting the known values:
\[
36^\circ + 36^\circ + \text{Angle N} = 180^\circ
\]
Combining the angles:
\[
72^\circ + \text{Angle N} = 180^\circ
\]
Now, subtract 72 degrees from both sides:
\[
\text{Angle N} = 180^\circ - 72^\circ
\]
\[
\text{Angle N} = 108^\circ
\]
So, the measures of the angles are:
- Angle M = 36 degrees
- Angle L = 36 degrees
- Angle N = 108 degrees