Triangle ABC is similar to triangle LMN by the AA Similarity Postulate. Also, m∠A = 129° and m∠C = 2 (m∠M). What is m∠M?

Again, this is a triangle so the sum of the angles must be 180°, so we can say:

a+b+c=180, we are told a=129, b=2c, we will let c=M°

129+2c+c=180 combine like terms on left side

129+3c=180 subtract 129 from both sides

3c=51 divide both sides by 3

c=17°

So angle M=17°