Determining the measure of indicated angles involves utilizing the relationships between angles within figures. The Angle Addition Postulate states that the sum of the angles in a triangle is 180 degrees, while the Triangle Sum Theorem extends this to any polygon. Angle bisectors divide angles into two congruent parts, and the Angle Bisector Theorem relates the lengths of the sides adjacent to the bisected angle. Complementary and supplementary angles have specific relationships, adding up to 90 or 180 degrees respectively. Understanding these angle properties enables finding unknown angle measures effectively.