Question

using the congruent complements or congruent supplements theorems
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 blank, 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 blank angles. then, using the blank property, the measure of angle 3 is blank degrees.

Explanation:

Step1: Recall congruent - complements theorem

If two angles are complements of the same angle, then they are congruent. Since ∠1 and ∠2 are complements and ∠2 and ∠3 are complements, by the congruent - complements theorem, ∠1≅∠3.

Step2: Use the definition of congruent angles

Congruent angles have equal measures. Since ∠1≅∠3, by the definition of congruent angles, m∠1 = m∠3.

Step3: Substitute the given value

Given that m∠1 = 35°, using the substitution property (if a=b and a = c, then b = c), we can substitute the value of m∠1 into the equation m∠1 = m∠3. So m∠3=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 property, the measure of angle 3 is 35 degrees.