Question

a. if the exterior sides of a pair of adjacent angles are perpendicular, then the angles are complementary. b. transitive property c. reflexive property d. a right angle is an angle with a measure of 90. e. perpendicular lines intersect to form four right angles. 20. given: ∠m≅∠r and ∠r≅∠z prove: ∠m≅∠z a. transitive property b. if two angles are supplementary to the same angle, then they are congruent. c. reflexive property d. definition of complementary angles e. definition of congruent angles. 21. an angles measure is 10 less than 4 times its complement. find the measure of the angle. a. 45 b. 70 c. 75 d. 90 e. none of the above 22. twice the complement of an angle is 50 less than the angles supplement. find the measure of the angle. a. 45 b. 50 c. 60 d. 90 e. none of the above

Explanation:

Step1: Recall angle - related properties for question 20

The transitive property of congruence states that if \(a\cong b\) and \(b\cong c\), then \(a\cong c\). Given \(\angle M\cong\angle R\) and \(\angle R\cong\angle Z\), by the transitive property, \(\angle M\cong\angle Z\).

Step2: Set up an equation for question 21

Let the angle be \(x\). Its complement is \(90 - x\). The equation is \(x=4(90 - x)- 10\).
Expand the right - hand side: \(x = 360-4x - 10\).
Add \(4x\) to both sides: \(x + 4x=360 - 10\), so \(5x=350\).
Divide both sides by 5: \(x = 70\).

Step3: Set up an equation for question 22

Let the angle be \(y\). Its complement is \(90 - y\) and its supplement is \(180 - y\). The equation is \(2(90 - y)=(180 - y)-50\).
Expand the left - hand side: \(180-2y=180 - y-50\).
Add \(2y\) to both sides and simplify: \(180=180 - y-50 + 2y\), so \(180=130 + y\).
Subtract 130 from both sides: \(y = 50\).

Answer:

1. A. Transitive Property
2. B. 70
3. B. 50