Two intersecting lines create four angles, numbered 1, 2, 3, and 4, where ∠4 is adjacent to ∠1 and ∠3, and m∠2=110°. Which other angle has a measure that is also equal to 110°?(1 point) ∠
The sum of the measures of the angles around a point (360 degrees) tells us that ∠1 + ∠2 + ∠3 + ∠4 = 360.
We are given that ∠2 = 110 degrees, so we can substitute this into the equation: ∠1 + 110 + ∠3 + ∠4 = 360.
We also know that ∠4 is adjacent to ∠1 and ∠3, so it must have the same measure as ∠1 and ∠3.
Let's call this common measure x. So, ∠4 = ∠1 = ∠3 = x.
The equation now becomes: x + 110 + x + x = 360.
Combining like terms, we have: 3x + 110 = 360.
Subtracting 110 from both sides, we get: 3x = 250.
Dividing both sides by 3, we get: x = 250/3.
So, the other angle that has a measure that is also equal to 110 degrees is ∠2, which means that ∠1, ∠2, ∠3, and ∠4 all have a measure of 110 degrees.