Concept explainers
(a)
Find the number of possible
(a)

Answer to Problem 40PPS
56
Explanation of Solution
Given:
Calculation:
There are total 8 angles.
The choices for first angle are 8 and for the second angle are 7 , since the pairings of angles cannot contain same angles .
So, the total number of choices are =
(b)
Describe the possible relationships between the measures of the angles in each pair.
(b)

Answer to Problem 40PPS
They can be congruent or supplementary.
Explanation of Solution
Given:
Calculation:
If the pairs of angles are corresponding angles , alternate interior angles , alternate exterior angles, vertically opposite angles , then they are congruent.
The pair of angles are supplementary , if they form linear pair, consecutive interior angles on the same side of transversal , angles that lie on the outer side of the parallel lines but on same side of transversal , or any combination.
(c)
Describe the likelihood of randomly selecting a pair of congruent angles.
(c)

Answer to Problem 40PPS
Explanation of Solution
Given:
The two levels of the bridge are parallel.
Calculation:
Since the pairs of corresponding angles and vertically opposite angles are congruent, so,
For the pairs of congruent angles,
The first angle has 8 choices , and the second angle has 3 choices , since 4 angles are congruent to one another , and both the angles in a pair cannot be same.
So, the choices are
The total number of pairs of angles are 56 , from part (a).
So, the probability that a randomly chosen pair of angle has congruent angles is
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