Answer:
25
Step-by-step 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.
