Question

Lines I and M are parallel.
What is the measure of angle 3?

Answer 1

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.