Answer:
1. ∠1 is the sum of ∠2 and another non-zero angle, so must be greater than ∠2.
2. ∠1 is the sum of ∠2 and another non-zero angle, so must be greater than ∠2.
Explanation:
1. ∠1 is an external angle to the triangle, so is the sum of the measures of the opposite internal angles. That is, ...
... ∠1 = ∠2 + ∠3
If we say ∠3 > 0, then we can rewrite the above equation as ...
... ∠3 = ∠1 - ∠2
Substituting into ...
... ∠3 > 0
we have ...
... ∠1 - ∠2 > 0
Adding ∠2 gives ...
... ∠1 > ∠2
2. ∠1 = ∠2 + ∠4, because both ∠1 and the angle sum are opposite interior angles where a transversal crosses parallel lines. By the same logic used above (replacing ∠3 with ∠4 in the development), ...
... ∠1 > ∠2