Question

Help fast thanks In the figure, prove that m∥n

Complete the proof below by providing the reasons in each blank.

Blank # 1

Blank # 2

Blank # 3

Answer 1

Explanation:

It is called adjacent angles to all pairs of angles (2 angles) that are consecutive (that is, have the vertex and one side in common) and supplementary ( the sum of both angles results in 180 °; that is, a straight angle). Graphically, two opposite semi-lines are observed. You can see two adjacent angles in the image.

A case of consecutive angles is shown between a"" and 133 °, because they form a straight angle and are separated by a common side. Then "a" and 133 ° add up to 180 °. In this way you can know what is the value of "a".

a+133°=180°

a=180°-133°

a=47°

The relative position of the angles with respect to the straight lines makes those angles receive specific names. Thus, it is called corresponding angles to those that are located on the same side of the parallels and on the same side of the transversal. These angles are equal.

Note that the other angle given as data is 47 °. This angle has the same value as "a" and as both angles are on the same side of the transverse, so that they are corresponding m must be parallel to n.

Answer 2

See below

Explanation:

a + 133 = 180 because they are supplementary angles. (adjacent angles that form a straight angle)

a = 47 (you substract 133 at each side of the previous equation, leaving that a = 47)

m || n Since "a" measure the same as the angle in the figure that measures 47 both are corresponding angles, therefore m and n are parallels