232k views
3 votes
Can I please get some help finding the measure of angle LNO?!?!? Please answer fast :)

Can I please get some help finding the measure of angle LNO?!?!? Please answer fast-example-1

1 Answer

7 votes

Answer:

40°

Explanation:

You want the measure of ∠LNO, marked as y°, given the two vertical angle pairs {100°, (x -y)°} and {y°, 2/7x°}.

Vertical angles

Vertical angles have the same measure, so we can write the equations ...

  • 100° = (x -y)°
  • y° = 2/7x°

Solution

We want the value of y, so it makes sense to solve these equations using a method that eliminates x. Rewriting the second equation to solve for x, we have ...

x° = 7/2y°

Substituting this into the first equation gives ...

100° + (7/2y -y)°

100° = 5/2y°

2/5(100) = y° = 40°

The measure of ∠LNO is 40°.

User Oroom
by
8.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.