Question

(see image for question)

Answer 1

65 degrees

Explanation:

The angle in question, when added to the corresponding angle outside the triangle, will equal 180 degrees. Therefore:

180 = (7x+10) + ∠ABC

∠ABC = 180 - (7x+10) = 170 - 7x

Now, the sum of the angles inside the triangle will also add to equal 180. To find the measure of ABC, we must first solve the triangle for x:

180 = (170-7x) + (2x+40) + (3x)

180 = 210-2x

x = (180-210)/-2 = 15

Now, input x into ABC to get the degree measure.

ABC = 170 - 7(15) = 170 - 105 = 65 degrees.

Hope this helped!

Answer 2

65 degrees

Explanation:

triangle exterior angle theorem states that the exterior angle of a triangle is equivilant to the opposite 2 interior angles

apply therorem to get equation:

7x+10= (2x+40)+ (3x)

solve for x

7x+10= 5x+40

2x+10= 40

2x= 30

x=15

angle ABC is 180- (7x+10)

=180 -(7(15)+10)

=180 -( 105+10)

=180 -115

=65