Question

Anyoneee help im stuck !! 15 points!!

Answer 1

Answer:

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!