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3 years ago

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

1 answer:

Nostrana [21]3 years ago

7 0

On this picture is shown a quadrilateral inscribed in a circle and by the Inscribed Quadrilateral Theorem the angles on the opposite vertices are supplementary, or in other words are equals to 180 degrees.

On this exercise it is asked to find the measure of angle B, First of all, you need to find the value of x. To so you have to select two opposite angles on this case angles A and C.

m<A+m<C=180 Substitute the given values for angles A and C
x+2+x-2=180 Combine like terms
2x=180 Divide by 2 in both sides to isolate x
x=90

Now, that the value of x is known you can substitute it in the expression representing angle D, and then subtract that number from 180 to find the measure of angle B.

m<D=x-10 Substitute the value of x
m<D=90-10 Combine like terms
m<D=80

m<B=180-m<D Substitute the value of angle D
m<B=180-80 Combine like terms
m<B=100

The measure of angle B is 100 degrees, and the value of x is 90.

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What are the expressions?

Romashka [77]

<h2>Explanation:</h2>

Here we need to solve some expressions. Remember the following rules:

$(+)(+)=+ \\ \\ (-)(-)=+ \\ \\ (+)(-)=- \\ \\ (-)(+)=-$

Then, from the left side:

$5-2\cdot 7=5-14=\boxed{-9} \\ \\ 5-2\cdot 4=5-8=\boxed{-3} \\ \\ 5-2\cdot 0=5-0=\boxed{5} \\ \\ 5-2\cdot -3=5+6=\boxed{11} \\ \\ 5-2\cdot 10=5-20=\boxed{-15} \\ \\ 5-2\cdot -8=5+16=\boxed{21} \\ \\$

from the right side:

$-(-4)+3=4+3=\boxed{7} \\ \\ -(6)+3=-6+3=\boxed{-3} \\ \\ -(-8)+3=8+3=\boxed{11} \\ \\ -(-5)+3=5+3=\boxed{8} \\ \\ -(2)+3=-2+3=\boxed{1} \\ \\ -(15)+3=-15+3=\boxed{-12} \\ \\ -(-6)+3=6+3=\boxed{9}$

4 0

3 years ago

The radius of a semicircle is 3 kilometres. What is the semicircle's perimeter?

alina1380 [7]

Answer:

In terms of Pi: $3\pi + 6$ km

Exact value (rounded): 15.42477 km

Approximated (3.14): 15.42 km

Step-by-step explanation:

Hello!

A semicircle's perimeter can be found using the formula: $P = \pi r + 2r$

We can plug in the values to solve for the perimeter.

<h3>Solve</h3>

$P = \pi r + 2r$
$P = \pi(3)+ 2(3)$
$P = 3\pi + 6$

In terms of Pi, it is $3\pi + 6$ ,

Exact value of Pi, it is 15.42477

Approximation of Pi (3.14), it is = 15.42

6 0

1 year ago

What the value of 4x - 6y x=3 y=-2

earnstyle [38]

Answer:

24

Step-by-step explanation:

Substituting...

4(3) - 6(- 2)

12 + 12

24

5 0

3 years ago

The ratio of water to punch mix is 8 parts to 1 part. If you use 6 gallons of water predict the amount of punch mix to use

Valentin [98]

Answer:

The amount of punch mix to use is 3/4 gallons

Step-by-step explanation:

Let

x ----> parts of water

y ---> parts of punch mix

we know that

$\frac{x}{y} =\frac{8}{1}$

$x=8y$ ----> equation A

That means ---> The parts of water is 8 times the parts of punch mix

If we have 6 gal of water

then

$x=6\ gal$

substitute in the equation A

$6=8y$

solve for y

$y=\frac{6}{8}\ gal$

Simplify

$y=\frac{3}{4}\ gal$

therefore

The amount of punch mix to use is 3/4 gallons

6 0

3 years ago

A bank loans a family $90,000 at 4.5% annual interest rate to purchase a house. The family agrees to pay the loan off by making

Naily [24]

Using it's formula, it is found that the monthly payment should be of $688.49 in order to pay off the debt in 15 years.

<h3>What is the monthly payment formula?</h3>

It is given by:

$A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}$

In which:

P is the initial amount.

r is the interest rate.

n is the number of payments.

For this problem, the parameters are given as follows:

A = 90000, r = 0.045, n = 15 x 12 = 180.

Hence:

r/12 = 0.045/12 = 0.00375.

Then we solve for A to find the monthly payment, as follows.

$A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}$

$A = 90000(0.00375)\frac{(1.00375)^{180}}{(1.00375)^{180} - 1}$

A = $688.49

More can be learned about the monthly payment formula at brainly.com/question/22846480

#SPJ1

4 0

2 years ago