Question

write a paragraph proof for the following. given: m∠abc = 114 m∠dhe = 25 m∠ehf = 41 ∠abc and ∠ghf are supplementary. prove: ∠dhf ≅ ∠ghf by the angle addition postulate, m∠dhf = . by the definition of supplementary angles, ∠dhf is supplementary to because the sum of their measures is . since is also supplementary to ∠abc, ∠dhf ≅ ∠ghf by the congruent theorem. (do not include the degree symbol in your answer.)

Explanation:

Step1: Calculate m∠DHF using Angle - Addition Postulate

m∠DHF=m∠DHE + m∠EHF=25 + 41 = 66

Step2: Recall supplementary - angle property

Since ∠ABC and ∠GHF are supplementary, and m∠ABC = 114, then m∠GHF=180 - 114 = 66.

Step3: Apply Congruent Supplements Theorem

∠DHF and ∠GHF are both supplementary to ∠ABC. By the Congruent Supplements Theorem, if two angles are supplementary to the same angle, then they are congruent.

Answer:

66; ∠ABC; 180; ∠GHF; Supplements