207k views
2 votes
(see image for question)

(see image for question)-example-1
User CMS Critic
by
8.1k points

2 Answers

5 votes

Answer:

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!

User Masoud Ramezani
by
8.2k points
4 votes

Answer:

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

User Ocasta Eshu
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories