Question

Anyoneee help im stuck !! 15 points!!

Answer 1

Given:
`\angle 1`,
`\angle 2`,
`\angle 3`,
`\angle 4` formed by two intersecting segments.

In the given figure;

Linear pair states that a pair adjacent angle formed when two lines intersect.

Then by definition of linear pairs,

`\angle 1` and
`\angle 2` forms a linear pair

Also,
`\angle 2` and
`\angle 3` forms a linear pair.

Linear pair postulates states that the two angle that forms a linear pair are supplementary(i,e add up to 180 degree).

Then by linear pair postulates;

`m\angle 1+ m\angle 2 =180^(\circ)`

and

`m\angle 2+m \angle 3 =180^(\circ)`

Substitution property of equality states that if x =y then, x can be substituted in for y or vice -versa.

then by substitution property of equality:

`m\angle 1+m\angle 2=m\angle 2+ m\angle 3`

Addition property of equality states that:

if x =y, then x + z = y+ z

By addition property of equality:

`m\angle 1 =m\angle 3` hence proved!