Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work.

Mathematics

1 answer:

Sveta_85 [38]3 years ago

3 0

Your statement that angle C and angle D adding to 180 degrees isn't always true. What is always true is that angle A and angle C add to 180 degrees.

Rule: The opposite angles of an inscribed quadrilateral are supplementary (add to 180 degrees)

So,
(angle A) + (angle C) = 180
(x+2) + (x-2) = 180
x+2+x-2 = 180
2x = 180
2x/2 = 180/2
x = 90

Once you know x, you can find the angles
measure of angle A = x+2
measure of angle A = 90+2
measure of angle A = 92 degrees

measure of angle C = x-2
measure of angle C = 90-2
measure of angle C = 88 degrees

Note how A+C = 92+88 = 180

measure of angle D = x-10
measure of angle D = 90-10
measure of angle D = 80 degrees

measure of angle B = 360-A-C-D ... see note below
measure of angle B = 360-92-88-80
measure of angle B = 100 degrees

Note: for any quadrilateral, the four angles add to 360 degrees. So A+B+C+D = 360. We can solve for B to get B = 360-A-C-D

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Hilary is given the pattern 2, 4, 6, 8, 10,... on her test. She has to find the 50th term of the pattern. To do so she needs to

natka813 [3]

Answer: A recursive formula would be best to describe the pattern.

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The common difference in the sequence above is 2. Upon close observation we would observe that by simply adding 2 to a number we can arrive at the next number.

However, using words to describe the pattern of the sequence would not be helpful if we have to find a number very far into the sequence, for example if we were to find the 1000th term of the sequence.

A recursive formula is preferable and would be the best option because of its simplicity in application. The recursive formula to calculate the nth term of an arithmetic progression is given as

nth = a + (n - 1)d

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The 50th term can be calculated as follows;

nth = 2 + (50 - 1)2

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The calculation above shows how simple it is to calculate the nth term with a recursive formula rather than with verbal descriptions.

An explicit formula also allows you to find the value of any term in a sequence. The explicit formula designates the nth term of the sequence as an expression of n, that is, it defines the sequence as a formula in terms of n. This formula lets us find any other term without knowing other terms.

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3 years ago

What us the approximate length of the diameter,d?

zhenek [66]

$\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r = radius\\[-0.5em] \hrulefill\\ C=44 \end{cases}\implies 44=2\pi r\implies \cfrac{44}{2\pi }=r\implies \cfrac{22}{\pi }=r \\\\\\ \stackrel{\textit{diameter is 2r}}{2\cdot \cfrac{22}{\pi }}\implies \cfrac{44}{\pi }\qquad \approx \qquad 14.00563499208679$