Whenever two or more lines intersect at a point, an angle is usually produced. And some of these angles formed may have common properties, and thus be congruent.
The appropriate reasons for the given statements in the question are given below:
STATEMENT REASON
1. <1 ≅ <2 Vertical Angle theorem
2. <1 and <2 are complementary
<2 and <3 are complementary Congruent Complements Theorem
3. <1 and <2 are supplementary
<2 and <3 are supplementary Congruent Supplements
4. <1 and <2 are right angles All Right Angles are Congruent
5. <1 ≅ <2,
<1 and <2 are supplementary If two angles are congruent and
supplementary, then each angle is
a right angle.
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