Triangle ABC is similar to triangle QRS by the AA Similarity Postulate. Also, m∠A = 32° and m∠S = 102°. What is m∠B?

The sum of interior angles of any polygon is:

s=180 (n-2)

Since we are dealing with a triangle:

s=180 (3-2)

s=180°

That is, the sum of angles of any triangle is 180°.

In this case we are given two angles with measures of 32° and 102° so

a+b+c=180

32+b+102=180 combine like terms on left

b+134=180 subtract 134 from both sides

b=46°