8-Find the measure of ∠CED.A. 52 °B. 48 °C. 42 °D. 32°
1 answer:
Measurement of ∠CED is ° with the help of vertically opposite angles.
To find out the angle which is to be found first let's understand the vertically opposite angle first:
What are vertically opposite angles?
Vertically opposite angles are angles that are opposite each other at a particular vertex and are formed by two straight intersecting lines.
Vertically opposite angles are equal to each other.
They are sometimes called vertical angles.
When two lines intersect, the opposite angles formed as a result of the intersection are called vertical or vertically opposite angles. A pair of vertically opposite angles are always equal. Also, a vertical angle and its adjacent angle are always complementary, i.e. they add up to degrees. For example, if two lines intersect and form an angle, say X=
°, then its opposite angle is also equal to
°. And the angle adjacent to X will be equal to
°.
Now according to the question
∠BED=°
And also ∠BED=∠BEC+∠CED
∠CED=∠BED-∠BEC
Hence ∠CED=°-
°
where ∠BEC and ∠AEF are vertically opposite angles.
Hence ∠CED=°
Learn more about vertically opposite angles here:
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9514 1404 393
Answer:
- ratio: 2
- sum: 765
- product: 1,761,205,026,816
Step-by-step explanation:
The general term of a geometric sequence is ...
an = a1×r^(n-1)
Here, we're given that the first term is a1 = 3. From the 8th term, we can find the common ratio, r.
a8 = 384 = 3r^7
128 = r^7 . . . . . . . . divide by 3
2 = r . . . . . . . . . 7th root
The common ratio is 2.
__
The sum of the terms of a geometric series is ...
Sn = a1×(r^n -1)/(r -1)
For the known values of a1 and r, the sum o 8 terms is ...
S8 = 3×(2^8 -1)/(2 -1) = 3(255) = 765
The sum of the first 8 terms is 765.
__
The product of the first 8 terms will be ...
(3)(3×2)(3×2^2)(3×2^3)...(3×2^6)(3×2^7) = (3^8)(2^(1+2+3+...+7))
= (3^8)(2^28) = 6561 × 268,435,456
Many calculators cannot report the full value of this product. (Many spreadsheets can.)
The product of the first 8 terms is 1,761,205,026,816.
_____
In the attached, we found the value of r that made the 8th term be 384 by solving the equation 3×r^7 -384 = 0. The value is shown on the graph as the x-intercept of the exponential function. That x-intercept is 2, so r=2 (as above).
