(a.) The triangles presented in this problem are congruent. We can prove this using the AAA (angle-angle-angle) theorem of similarity. This states that if all three angles of a triangle are equivalent then the sides of the triangles are proportional. We know that all three angles of these triangles are the same since the image shows angle A = angle P, and angle B = angle Q, therefore, angle C = angle R.
(b.) Now that we know the triangles are similar and the sides are proportional, we can simply take a ratio of the sides to solve for x.
(3x+6)/24 = 28/32 3x+6 = (28/32)(24) 3x = 21 - 6 x = 15/3 x = 5
