Question

first quarter seton test 3 (test includes material up to lesson 21. take after lesson 21.) 1. (l15) complementary angles are angles whose measures add up to ____ degrees. a. 180 b. 45 c. 360 d. 90 e. not applicable 2. (l20) is the following sentence true? if the exterior sides of a pair of adjacent angles are perpendicular, then the angles are equal a. yes b. no c. depends on the exterior sides d. either a or c e. none of the above 3. (l2) the following argument is a(n) __ deduction: if two angles are supplementary to the same angle, then they are congruent. if ∠a and ∠b are supplementary to each other, then they are congruent. a. valid b. invalid c. not enough data to determine d. neither a nor b e. none of the above 4. (l4) the following argument is a(n) ____ deduction. adjacent angles are angles that have the same vertex, share a common side, and have no interior points in common. since ∠1 and ∠2 do not share a common side, they are not adjacent. a. valid b. invalid c. not enough data to determine d. neither a nor b e. none of the above

Explanation:

1. By definition, complementary angles have measures that sum to 90 degrees.
2. If the exterior sides of a pair of adjacent angles are perpendicular, the angles are complementary but not necessarily equal.
3. The statement "If two angles are supplementary to the same angle, then they are congruent" is a valid geometric property, but the second - part "If ∠A and ∠B are supplementary to each other, then they are congruent" is wrong as supplementary angles add up to 180 degrees and are not necessarily congruent, so the overall deduction is invalid.
4. Since the definition of adjacent angles requires sharing a common side and ∠1 and ∠2 do not share a common side, the deduction that they are not adjacent is valid based on the definition.

Answer:

1. D. 90
2. B. No
3. B. invalid
4. A. valid