6x+y=-2 in slope-intercept form
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Based on the calculations, the measure of angle BDF and CFG are 100° and 38° respectively.
<h3>The condition for two parallel lines.</h3>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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The law of sines can be used to find the missing side lengths.
... RP = sin(60°)/sin(45°)·10 = 10√(3/2) ≈ 12.247
... PS = sin(75°)/sin(45°)·10 ≈ 13.660
Then the perimeter is
... perimeter = RS + RP + PS
... = 10 + 12.247 + 13.660 ≈ 35.91 . . . .units
