60.1k views
1 vote
Lines I and M are parallel.
What is the measure of angle 3?

Lines I and M are parallel. What is the measure of angle 3?-example-1
User Harry Kim
by
8.1k points

1 Answer

6 votes

Answer:

25

Explanation:

By the vertical angle theorem, we can find that:

m∠1 = 85

By the corresponding angle theorem, we can find that:

m∠2 = 2x

By the alternate interior angle theorem, we can find that:

m∠3 = x - 10

We also know that angles 1, 2, and 3 are the measures of the angles of a triangle. So:

85 + 2x + (x - 10) = 180

Lets solve for x. Combine like terms.

75 + 3x = 180

Subtract 75 from both sides.

3x = 105

Divide both sides by 3.

x = 35

So now we know that x + 35. Knowing this, we can find the measure of angle 3 by plugging 35 for x in x - 10

m∠3 = 35 - 10 = 25

So the measure of angle 3 is 25.

I hope this helps. Happy studying.

User Muhammad Younas
by
7.9k 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