If triangle rst is an acute triangle, then m∠s must be? less than 90°. equal to 90°. equal to 100°. greater than 90° and less than 180°.

m∠S must be less than 90° ⇒ first answer

Step-by-step explanation:

* Lets talk about the types of the triangles according to the measures

 of their angle

- The acute angle triangle:

# Its three angles are acute angles

- The right angle triangle

# One of its angle is right angle and the two other angles are acute

- The obtuse angle triangle

# One of its angle is obtuse angle and the other two angles are acute

- From all above any triangle has at least two acute angles

* Lets revise the measure of the angles

- The measure of any acute angle is greater than 0° and less than 90°

- The measure of the right angle is 90°

- The measure of any obtuse angle is greater than 90° and less

  than 180°

* Lets solve the problem

∵ Triangle RST is an acute triangle

∴ Its three angles are acute angles

∵ The measure of the acute angle is less than 90°

∴ The measures of the three angles is less than 90°

∴ m∠S must be less than 90°

∠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.