Question

Which of the following statements help to prove that Calypso Rd. and Capoeira Rd. are parallel?

Select all that apply.
a) m∠2 =81∘ and m∠3=89∘
b) m∠1=90∘ and m∠5=90∘
c) m∠4=85∘ and m∠4=85∘
d) m∠2 + m∠6 = 180∘

Answer 1

Statement d) m∠2 + m∠6 = 180∘ helps prove that Calypso Rd. and Capoeira Rd. are parallel.

Step-by-step explanation:

In order to prove that Calypso Rd. and Capoeira Rd. are parallel, we need to identify statements that indicate parallel lines or angles. Let's analyze each statement:

1. Statement a) m∠2 = 81∘ and m∠3 = 89∘: These angle measures do not provide any information about parallel lines.
2. Statement b) m∠1 = 90∘ and m∠5 = 90∘: A pair of perpendicular lines can also form right angles, so this statement does not prove parallelism.
3. Statement c) m∠4 = 85∘ and m∠4 = 85∘: This statement implies that angles are congruent, but it does not provide evidence of parallel lines.
4. Statement d) m∠2 + m∠6 = 180∘: This statement implies that angle 2 and angle 6 are supplementary angles, which is a characteristic of corresponding angles on parallel lines. Therefore, statement d helps prove that Calypso Rd. and Capoeira Rd. are parallel.

Based on our analysis, the correct statement that helps prove that Calypso Rd. and Capoeira Rd. are parallel is statement d) m∠2 + m∠6 = 180∘.