Atriangle has a 90° angle, and the other two interior angles are congruent. explain how to find the measure of one of the two congruent angles.

well  we already know that a triangle degree is 180 and we already have one degrees angle which is 90 so in order to figure it out we'll have to subtract them both:

180 - 90= 90

were left with 90 now we know that the other two angles are going to be some what equal to 90 and since the two angles are "congruent" meaning its going to be half. therefore, were going to divide it by half (2)

90/2 = 45

45 is your answer  :D

~batmans wife dun dun dun

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∠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.