Question

complementary and supplementary angles
instruction active
using the congruent complements or congruent supplements theorems
given: ∠1 and ∠2 are complements,
∠2 and ∠3 are complements, and $m\angle1 = 35^\circ$.
prove: $m\angle3 = 35^\circ$
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 refers to the theorem that states if two angles are complements of the same angle, they are congruent. This is the Congruent Complements Theorem.
2. The definition of congruent angles states that their measures are equal, so this fills the second blank.
3. The transitive (or substitution) property allows us to replace the measure of ∠1 with 35° to find the measure of ∠3, as they are equal.
4. Given \(m\angle1 = 35^\circ\) and \(m\angle1 = m\angle3\), the measure of ∠3 is 35°.

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 (or transitive) property, the measure of angle 3 is 35 degrees.