Question

given: ∠1 and ∠2 are complements, ∠2 and ∠3 are complements, and m∠1 = 35° prove m∠3 = 35° complete the missing parts of the paragraph proof. by the △, we know that angle 1 is congruent to angle 3. the measure of angle 1 equals the measure of angle 3 by the definition of △ angles. then, using the △ property, the measure of angle 3 is △ degrees

Explanation:

1. The first blank: When two angles are complements of the same angle (or congruent angles), they are congruent. This is the "Complements of the same angle are congruent" theorem (or "Congruent Complements Theorem"). So we use this theorem to say ∠1 ≅ ∠3.
2. The second blank: Congruent angles have equal measures by the definition of congruent angles.
3. The third blank: Since m∠1 = 35° and m∠1 = m∠3 (from congruent angles), we use the substitution property (substituting m∠1 with 35° to find m∠3).
4. The fourth blank: Since m∠1 = 35° and m∠3 = m∠1, then m∠3 = 35° by substitution.

Answer:

First dropdown: Complements of the same angle are congruent (or Congruent Complements Theorem)
Second dropdown: congruent
Third dropdown: substitution
Fourth dropdown: 35