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. First, when two angles are complements of the same angle, they are congruent. This is the Congruent Complements Theorem, which applies here since ∠1 and ∠3 are both complements of ∠2.
2. Congruent angles are defined as angles that have equal measures, so this justifies that \( m\angle1 = m\angle3 \).
3. The substitution property allows us to replace \( m\angle1 \) with its given value of 35° to find \( m\angle3 \).

Answer:

By the Congruent Complements Theorem, 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 congruent angles. Then, using the substitution property, the measure of angle 3 is 35 degrees.