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When two parallel lines are intersected by a transversal, the same-side exterior angles are supplementary. That means that their sum is 180.
Using that logic, if the two roads were parallel, then the sum of their same-side exterior angles will add up to 180. Yet their same-side exterior angles add up to 170 (130 + 40 = 170), hence they can't be parallel.
See the drawing attached below.
Using supplmenatry angles (two angles whose sum of measures add up to 180 or a straight line), we can say that:
m<DIE + m<HID = 18
40 + m<HID = 180
m<HID = 140
Similarly:
m<BHC + m<CHI = 180
130 + m<CHI = 180
m<CHI = 50
Using verticle angles therome, (when two lines intersect, the angles opposite to eachother are congruent, or have the same measure), we can say that:
m<DIE = m<GIH = 40
m<GIE = m<HID = 140
m<CHI = m<AHB = 50
m<BHC = m<AHI = 130
Answer:
x = -1 ± √6 / 5
Step-by-step explanation:
Solve + 2x = 1
move 1 to the left side of the equation by subtracting it from both sides.
+ 2x - 1 = 0
Use the quadratic formula to find the solutions.
-b± / 2a
Substitute the values a = 5 , b = 2, and c = -1 into the quadratic formula and solve for x
-2±/ 2 ⋅ 5
Simplify.
x = -2 ± 2 / 10
x = -1 ± / 5
Exact Form:
x = -1 ± / 5