Fill in each blank with a true statement

See below.

Step-by-step explanation:

7.)

Supplementary angles add up to 180°. ∠B's supplement is 22°. This means ∠B is 158°. Since ∠A ≅ ∠B, the m∠A = 158°.

8.)

Again, supplementary angles add up to 180°. ∠P is a right angle meaning it is 90°. Therefore, the m∠Q is 90° as well.

9.)

Complementary angles add up to 90°. In order for ∠S and ∠T to be complementary, they both need to angle measurements less than 90° meaning they both need to be acute angles.

Now that we know that ∠T is acute, the only way ∠U can be its supplement is if it has an angle measure greater than 90°. Therefore, ∠U is an obtuse angle.

10.)

Similar to question 9, if an angle is obtuse, its supplement must be an acute angle.

it 2

step-by-step explanation:

8^1/3=2

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.