Find m abc (6x-7) (4x+23)
1 answer:
Answer:
m∠ABC = 83°
Step-by-step explanation:
The angle ∠abc and ∠dbe are opposed by the vertex. By definition "<em>Two angles opposite the vertex are congruent or equal</em>"
So ∠abc = ∠dbe
Then, to solve this problem you must match both expressions and clear the variable x.
Now substitute x = 15 in the given expression for the angle ∠abc. (6x-7)
So, we have:
°
Finally, the angle is 83°
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Answers:
(1) Option (B) 60.
(2) Option (C) 946.4 yd^2.
(3) D<span>egree of the central angle for sector C = </span>126°.
Explanations:
(1) The original area of parallelogram is = A = 120
Since
Area-of-parallelogram = (base)(height)
A = bh = 120
Now the base is reduced to one-fourth of its original length and height is doubled. Therefore the new Area will be:
Since bh = 120 (as stated above); therefore:
So the new Area will be 60.
(2) The area of a regular polygon = Area = (1/2)(apothem) (perimeter).
perimeter = 8 * (side-length) = 8(14) = 112 yards
(8 because it's octagon)
Area = (1/2)(apothem) (perimeter)Area = (1/2)(16.9) (112)Area = 946.4 yd^2
(3) For this you need to know the sector-angle formula:
(Area-of-a-given-sector) / (Total Area) = (Degrees-of-the-central-angle)/(Total-degrees)
Area-of-a-given-sector = 0.35
Total Area = 0.35 + 0.15 + 0.5 = 1.0
Degrees-of-the-central-angle = ?
Total Degree = 360°
Plug in the values in equation:
0.35/1 = (Degrees-of-the-central-angle)/360°
=> Degrees-of-the-central-angle = 0.35 * 360° = 126°
(1) Option (B) 60.
(2) Option (C) 946.4 yd^2.
(3) D<span>egree of the central angle for sector C = </span>126°.
Explanations:
(1) The original area of parallelogram is = A = 120
Since
Area-of-parallelogram = (base)(height)
A = bh = 120
Now the base is reduced to one-fourth of its original length and height is doubled. Therefore the new Area will be:
Since bh = 120 (as stated above); therefore:
So the new Area will be 60.
(2) The area of a regular polygon = Area = (1/2)(apothem) (perimeter).
perimeter = 8 * (side-length) = 8(14) = 112 yards
(8 because it's octagon)
Area = (1/2)(apothem) (perimeter)Area = (1/2)(16.9) (112)Area = 946.4 yd^2
(3) For this you need to know the sector-angle formula:
(Area-of-a-given-sector) / (Total Area) = (Degrees-of-the-central-angle)/(Total-degrees)
Area-of-a-given-sector = 0.35
Total Area = 0.35 + 0.15 + 0.5 = 1.0
Degrees-of-the-central-angle = ?
Total Degree = 360°
Plug in the values in equation:
0.35/1 = (Degrees-of-the-central-angle)/360°
=> Degrees-of-the-central-angle = 0.35 * 360° = 126°