Mathematics, 08.10.2019 03:00 kathleenirwin

which of the following statements prove that calypso rd and capoeira rd are parallel?

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Answer from: robert7248

Did anyone reply? pl let me know

Answer from: decorajackson01

The answers are given below.

Step-by-step explanation: We are given two straight lines calypso rd and capoeira rd. Both are cut with a transversal Lambda Ave. We are select all the correct conditions from the given options that will help to prove that lines calypso rd and capoeira rd are parallel to each other.

Condition (1) is

$m\angle 2=81^\circ,~~m\angle 3=89^\circ.$

Since ∠2 and ∠3 are interior angles on the same side of the transversal and their sum is 81° + 89° = 170° ≠ 180°, so this condition will not help.

Condition (2) is

$m\angle 1=90^\circ,~~m\angle 5=90^\circ.$

Since ∠1 and ∠3 are vertically opposite angles and ∠3 and ∠5 are corresponding angles, so we have m∠1 = m∠3 = m∠5, so this condition will help.

Condition (3) is

$m\angle 4=85^\circ,~~m\angle 5=85^\circ.$

Since the measurement of ∠4 and ∠5 do not have anything related to prove the parallelism of the given lines, so this condition will not help.

Condition (4) is

$m\angle 2+m\angle 6=180^\circ.$

Since ∠2 and ∠6 are corresponding angles, so their measurement shoul be equal in order to prove the lines parallel. vAs our given condition does not imply this, so this condition will also not help.

Condition (5) is

$m\angle 2+m\angle 3=180^\circ.$

Since ∠2 and ∠3 are interior angles on the same side of the transversal, and their sum is given to be 180°, so this condition implies that the two lines are parallel. Hence, this condition will help.

Condition (6) is

$m\angle 3+m\angle 4+m\angle 5+m\angle 6=360^\circ.$

Since this is the general condition that the measurement of the whole angle is 360°, so this condition will not help.

Condition (6) is

$m\angle 1=m\angle 3=m\angle 5.$

Since ∠1 and ∠3 are corresponding angles and ∠3 and ∠5 are alternate interior angles, so their equality will definitely help in proving the lines to be parallel.

Thus, the correct conditions are

$m\angle 1=90^\circ,~~m\angle 5=89^\circ.$

$m\angle 2+m\angle 3=180^\circ.$

$m\angle 1=m\angle 3=m\angle 5.$

Answer from: Quest

560

step-by-step explanation:

giggidy

Answer from: Quest

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!

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