9514 1404 393
Answer:
A: 1; B: 3; C: 2; D: 2; E: 4
Explanation:
The sum of angles in a triangle is 180°. This statement is called the "Triangle Sum Theorem."
Statement line 2 is a list of the three angles in the triangle. The one missing is angle S (tile 1, answer A). The missing theorem description is tile 3, answer B.
Statement lines 3 and 4 are algebra. Line 3 is a substitution of a number for the measure of angle Q. Since angle Q is marked as a right angle, its measure is 90° (tile 2, answer C). Line 4 subtracts that 90° from both sides of the equation, resulting in a statement that the sum of the two angles is 90° (tile 2, answer D).
Finally, we declare the angles complementary because we've shown their sum is 90°. That's a matter of definition. (tile 4, answer E).