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2 years ago

In the trapezoid at the right, BE= 2x-8, DE= x-4, and AC= x+2

Mathematics

1 answer:

Marta_Voda [28]2 years ago

5 0

Answer:

A. x = 5 (Equation below)

B. AC = 9 | BD = 9

Step-by-step explanation:

A. Since we know the diagonals of an isosceles trapezoid are congruent, we know that the two bottom parts of the diagonal BD (2x - 8 and x - 4) are congruent to the diagonal AC (x + 2) . This means you can just equal them together and get the value of x:

2x - 8 + x - 4 = x + 2

3x - 12 = x + 2

3x = x + 14

2x = 14

x = 7

B. Just plug in 5 for x:

AC = x + 2 = 7 + 2 = 9

BD = 2x - 8 + x -4 = 3x - 12 = 21 - 12 = 9

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In the figure, angle ZYX is measured in degrees. The area of the shaded sector can be determined using the formula StartFraction

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<u>The given options are:</u>

(A)the central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.

(B)the central angle measure of the sector divided by the total angle measure of a circle multiplied by the circumference of the circle will yield the area of the sector.

(C)the central angle measure of the sector multiplied by the area of the circle will yield the area of the sector.

(D)the central angle measure of the sector multiplied by the circumference of the circle will yield the area of the sector.

Answer:

(A)the central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.

Step-by-step explanation:

The area of the shaded sector can be determined using the formula:

$\frac{m\angle ZYX}{360^\circ} \cdot \pi r^2$

$m\angle XYZ=$Central angle of XYZ\\\pi r^2$=Area of a Circle$

$360^\circ =$Total Angle$

Therefore, the formula is:

$\dfrac{m\angle ZYX}{360^\circ} \cdot \pi r^2\\\text{Area of XYZ}=\dfrac{\text{Cental Angle of XYZ}}{\text{Total Angle}} X \text{Area of the Circle}$

Therefore, the formula is best explained by Option A.

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Step-by-step explanation:

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