Question

9 multiple choice 1 point ellie, sam, anna, and chris used their protractors to measure pairs of consecutive angles in trapezoid cats. they recorded their measurements in the following table. angles of a trapezoid student angle pair measures ellie ∠1 and ∠2 96° and 129.5° sam ∠2 and ∠3 130.5° and 49° anna ∠3 and ∠4 50° and 85° chris ∠4 and ∠1 86° and 94.5° using inductive reasoning, what might you conclude about consecutive angles of a trapezoid? there is no pattern they are congruent they are complementary they are supplementary

Explanation:

Step1: Calculate sum of Ellie's angle - pair

$96^{\circ}+ 129.5^{\circ}=225.5^{\circ}$

Step2: Calculate sum of Sam's angle - pair

$130.5^{\circ}+49^{\circ}=179.5^{\circ}$

Step3: Calculate sum of Anna's angle - pair

$50^{\circ}+85^{\circ}=135^{\circ}$

Step4: Calculate sum of Chris's angle - pair

$86^{\circ}+94.5^{\circ}=180.5^{\circ}$
We can see that the sums are not consistent with complementary (sum is $90^{\circ}$), congruent (equal measure), and there is no clear pattern. Also, the sums are close to but not exactly $180^{\circ}$ (supplementary). However, considering measurement errors in using protractors, we can make an inductive - reasoning conclusion.

Answer:

there is no pattern