Angles ∠1 and ∠3 are supplementary angles meaning that their measures must add to 180°.
Let's call the angles a and b. Angle a is ∠1 and angle b is ∠3. Now let's write what we know.
a = b - 10
a + b = 180
The first equation is solved for a, so we can plug b - 10 in for a in the secnd equation.
(b-10) + b = 180
2b - 10 = 180
2b = 190
b = 95
If b = 95, then we know that a = 95 - 10 = 85.
We know ∠1 and ∠2 are equal because they are alternate inferior angles. The same applies to ∠3 and ∠4.
The answer is D.
