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

$m\angle DHF=m\angle DHE + m\angle EHF=25 + 41=66$

Step2: Find m∠GHF

Since $\angle ABC$ and $\angle GHF$ are supplementary and $m\angle ABC = 114$, then $m\angle GHF=180 - 114 = 66$

Step3: Apply Congruent Supplements Theorem

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

Answer:

66; $\angle ABC$; 180; $\angle GHF$; Supplements