In Geometry, two (2) straight lines are considered to be parallel if their slopes are the same (equal) and they have different y-intercepts. This ultimately implies that, two (2) straight lines are parallel under the following conditions:

m₁ = m₂

<u>Note:</u> m is the slope.

<h3>What is the alternate interior angles theorem?</h3>

The alternate interior angles theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.

Based on the alternate interior angles theorem, we can infer and logically deduce the following properties from the diagram (see attachment):

<ABD = <BDH = 38°

<DFE = <HDF = 62°

For angle BDF, we have:

<BDF = <BDH + <HDF

<BDF = 38° + 62°

<BDF = 100°.

Since angles BDF and DFC are linear pair, they are supplementary angles. Thus, we have:

∠BDF + <DFC = 180°

<DFC = 180 - ∠BDF

<DFC = 180 - 100

<DFC = 80°.

For angle CFG, we have:

∠DFE + <DFC + <CFG= 180°

<CFG = 180° - ∠DFE - <DFC

<CFG = 180° - 62° - 80°

<CFG = 38°.

Read more on parallel lines here: brainly.com/question/3851016

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2 years ago