Answer:
28 degrees
Step-by-step explanation:
step 1
Find the measure of angle 1
[tex]m\angle 1+65^o=180^o[/tex] ----> by supplementary angles
[tex]m\angle 1=180^o-65^o=115^o[/tex]
step 2
Find the value of x
[tex](10x+5)^o=m\angle 1[/tex] ----> by corresponding angles
substitute
[tex](10x+5)^o=115^o[/tex]
[tex]10x=110\\x=11[/tex]
step 3
Find the measure of angle 2
Remember that the sum of the interior angles in any triangle must be equal to 180 degrees
[tex]m\angle 1+m\angle 2+(4x-7)^o=180^o[/tex]
substitute
[tex]115^o+m\angle 2+(4(11)-7)^o=180^o[/tex]
[tex]m\angle 2=180^o-152^o=28^o[/tex]
