Answer :
Answer:
The sum of the measures of ∠1 and ∠2 is 131 degrees
Step-by-step explanation:
The picture of the question in the attached figure
step 1
Find the measure of angle 1
In this problem Line p is parallel to segment BC
so
[tex]m\angle 1=57^o[/tex] ----> by alternate interior angles
step 2
Find the measure of angle 2
we know that
The sum of the interior angles in any triangle must be equal to 180 degrees
In the triangle ABC
[tex]m\angle 2+57^o+49^o=180^o[/tex]
[tex]m\angle 2=180^o-106^o=74^o[/tex]
step 3
Find the sum of the measures of ∠1 and ∠2
we have
[tex]m\angle 1=57^o[/tex]
[tex]m\angle 2=74^o[/tex]
so
[tex]m\angle 1+m\angle 2=57^o+74^o=131^o[/tex]
