A quadrilateral is inscribed in a circle. Find the measure of each missing angle as labeled below. explain answer please

9514 1404 393

Answer:

  1: 40°; 2: 110°; 3: 70°; 4: 45°; 5: 65°

  6: 70°; 7: 70°; 8: 65°; 9: 45°; 10: 17.5°

  11: 15°; 12: 37.5°; 13: 70°; 14: 72.5°; 15: 20°

  16: 87.5°; 17: 77.5°; 18: 35°; 19: 75°; 20: 20°

  21: 50°; 22: 95°

Step-by-step explanation:

The angles are shown in the attached. The following relationships are used to find them.

_____

All of the arcs around the circle are shown except EL and HN. EL is the difference between 180° and the other marked angles in semicircle SLH. It is 90°. HN has a vertical central angle with arc SE, so is the same measure, 40°.

Angle 1 is the central angle for arc HN, so has the same measure: 40°.

Angle 2 is half the sum of arcs SL and HW, so is (130+90)/2 = 110°.

Angle 3 is vertical to the second remote interior angle in triangle BDQ where angle 2 is an exterior angle. That is ∠3 = ∠2 -∠1 = 110° -40° = 70°.

Angle 4 is half arc NL, so is (40° +30° +20°)/2 =45°.

Angle 5 is the remaining interior angle of ∆BNW, so is 180° -70° -45° = 65°.

Angle 6 is half of arc HE, so is (30° +20° +90°)/2 = 70°.

Angle 7 is half of arc SN, so is 140°/2 = 70°.

  — note that triangle HNQ is an isosceles triangle with central angle 40°, so the two base angles (∠6 and ∠7) are (180° -40°)/2 = 70°.

Angle 8 is half the measure of arc LS, so is (90° +40°)/2 = 65°.

Angle 9 is half the measure of arc HW, so is (40° +50°)/2 = 45°.

Angle 10 is half the measure of arc ST, so is 35°/2 = 17.5°.

Angle 11 is half the measure of arc OT, so is 30°/2 = 15°.

Angle 12 is half the measure of arc NO, so is (50° +25°)/2 = 37.5°.

Angle 13 is half the measure of arc HE, so is 140°/2 = 70°.

Angle 14 is half the measure of arc HT, so is (180° -35°)/2 = 72.5°.

Angle 15 is half the measure of arc ES, so is 40°/2 = 20°.

Angle 16 is vertical to the remaining interior angle of the triangle containing angles 14 and 15. Its measure is 180° -72.5° -20° = 87.5°.

Angle 17 is half the sum of arcs ES and OH, so is (40° +115°)/2 = 77.5°.

Angle 18 is half the measure of arc RN, so is (30° +40°)/2 = 35°.

Angle 19 is half the sum of arcs LR and EW, so is (20° +130°)/2 = 75°.

Angle 20 is half the measure of arc HN, so is 40°/2 = 20°.

Angle 21 is complementary to angle 1, so is (90° -40°) = 50°.

Angle 22 is the remaining interior angle of triangle ACE, so is (180° -35° -50°) = 95°.

Answer:

2/33

Step-by-step explanation:

calculator.net

Answer:

.165, i think

.165×2 =.33

have a good day

Answer:

The correct answer is "9.3%".

Step-by-step explanation:

The given values are:

Amount of interest,

= $590

Principle,

= $8,000

Time:

= 285

Let the interest rate will be "x".

Now,

⇒  [tex]Amount \ of \ interest=Principle\times Interest \ rate\times \frac{time}{No. \ of \ days \ in \ year}[/tex]

On substituting the values, we get

⇒                             [tex]590=8000\times x\times \frac{285}{360}[/tex]

⇒                             [tex]590=6333.33\times x[/tex]

⇒                                [tex]x=\frac{590}{6333.33}[/tex]

⇒                                   [tex]=9.3157 \ percent[/tex]

or,

⇒                                   [tex]=9.3[/tex]%

Answer:

[tex]61.261 {ft}^{2} [/tex]

Step-by-step explanation:

[tex] \frac{270}{360} \times 2\pi \: r \\ \frac{270}{360} \times 2 \times \pi \times 13 \\ = 61.261 {ft}^{2} [/tex]

Answer5

Step-by-step explanation:

Answer:

18.9

Step-by-step explanation:

Answer:

Since P(male)xP(fail) = 0.0549 and and P(male and fail) = 0.0773, the two results are different, so the events are not independent.

Answer:

It is a negative slope :)

Answer:

316.41 m³

Step-by-step explanation:

7.5x7.5x3.75=210.9375

3.75x3.75x7.5=105.46875

210.9375+105.4675=316.405

Answer:

4.968

Step-by-step explanation:

Answer:

The three best can be chosen and ranked in 336 ways.

Step-by-step explanation:

Since you are asked to list the movies in order of preference, the order is important, as a higher order leads to a higher preference. This means that the permutations formula is used to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

If you saw eight movies this year, in how many ways can the three best be chosen and ranked?

[tex]P_{(8,3)} = \frac{8!}{(8-3)!} = 336[/tex]

The three best can be chosen and ranked in 336 ways.

Answer:

answer is b²a is the correct answer

Step-by-step explanation:

happy to help :)

Answer:

u already got it cos x = 8f

Step-by-step explanation:

Answer:

Step-by-step explanation:

Alternate interior angles:-

Pairs - <2 and <8 ; <3 and <5

Alternate exterior angles:-

Pairs - <1 and <7 ; <4 and <6

Answer:

58

Step-by-step explanation:

1).2+24+3 = 29

2) 29 x 2 = 58

Answer:

The shipping container's volume is 24 cubic feet.

Step-by-step explanation:

Being a rectangular box, you can find the volume of it by multiplying its length, width, and height together.

We're given the dimensions 4' x 2' x 3'.  If we multiply those we get (4 × 2 × 3)', or 24 cubic feet.  The box then has a volume of 24 cubic feet.

9514 1404 393

Answer:

  71.4

Step-by-step explanation:

The perimeter of the polygon is the sum of the lengths of its sides. Opposite sides in this geometry have the same sum, so the perimeter is ...

  P = 2(16.4 +19.3) = 2(35.7)

  P = 71.4 . . . units

__

The missing length on the lower half of the upper right side is 6.3.

Answer:

equation of a line

Step-by-step explanation:

Answer:

Formula used during line equations

Answer:

86 %

Step-by-step explanation:

Total no. of squares = 50

No. of green squares = 43

Percentage of green squares = (43/50) x 100%

Percentage = 86%

Answer:

Hope This Helps!

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

-3/8 converted to a decimal is -0.375

The absolute value of -0.5 is 0.5

hence, 0.5 is larger than -0.375

so the answer is d

hope this helps and is right :)

Answer:

Please look at the image.

Step-by-step explanation:

Answer:

overestimate = 7

underestimate = 5

Step-by-step explanation:

Table

_________________________________

Time (months)    0    1    2     3      4     5     6

Rate                   5   7     9    14    22    31    40

___________________________________

A. Make an overestimate and an underestimate of the total quantity of pollutants that escape during the first month.

Overestimate

For this case, we review the data in the table. The value for first month of total quantity of pollutants that escape is 7. Additionally, we can notice that the rate is increasing.

Just a month and that month has a value of  7

= 1* 7 (The largest value) = 7

Underestimate

This would be equivalent to the total until the previous meassure

= 1*5 = 5

Answer:

[tex] \displaystyle a_{1} = 108[/tex]

Step-by-step explanation:

we are given

the sum,common difference and nth term of a geometric sequence

we want to figure out the first term

recall geometric sequence

[tex] \displaystyle S_{ \text{n}} = \frac{ a_{1}(1 - {r}^{n} )}{1 - r} [/tex]

we are given that

thus substitute:

[tex] \displaystyle 189= \frac{ a_{1}(1 - {( \frac{1}{2} )}^{3} )}{1 - \frac{1}{2} } [/tex]

to figure out [tex]a_1[/tex] we need to figure out the equation

simplify denominator:

[tex] \displaystyle \frac{ a_{1}(1 - {( \frac{1}{2} )}^{3} )}{ \dfrac{1}{2} } = 189[/tex]

simplify square:

[tex] \displaystyle \frac{ a_{1}(1 - {( \frac{1}{8} )}^{} )}{ \dfrac{1}{2} } = 189[/tex]

simplify substraction:

[tex] \displaystyle \frac{ a_{1} (\frac{7}{8} )}{ \frac{1}{2} } = 189[/tex]

simplify complex fraction:

[tex] \displaystyle a_{1} (\frac{7}{8} ) \div { \frac{1}{2} } = 189[/tex]

calculate reciprocal:

[tex] \displaystyle a_{1} \frac{7}{8} \times 2 = 189[/tex]

reduce fraction:

[tex] \displaystyle a_{1} \frac{7}{4} \ = 189[/tex]

multiply both sides by 4/7:

[tex] \displaystyle a_{1} \frac{7}{4} \times \frac{4}{7} \ = 189 \times \frac{4}{7} [/tex]

reduce fraction:

[tex] \displaystyle a_{1} = 27\times 4[/tex]

simplify multiplication:

[tex] \displaystyle a_{1} = 108[/tex]

hence,

[tex] \displaystyle a_{1} = 108[/tex]

Answer:

The table is a quadratic function

Step-by-step explanation:

Given

The attached table

Required

Tell if it is a quadratic function

The difference in the x values are uniform (i.e. difference of 1), so the following method can be applied.

(1) Subtract adjacent y values.

[tex]d_1=2 - 16 = -14[/tex]

[tex]d_2=-2 - 2 = -4[/tex]

[tex]d_3 = 4--2 = 6[/tex]

[tex]d_4 = 20 - 4 = 16[/tex]

(2) Subtract adjacent differences in (1) above

[tex]d_5 = d_2 - d_1 = -4 --14 = 10[/tex]

[tex]d_6 = d_3 - d_2 = 6 --4 = 10[/tex]

[tex]d_7 = d_4 - d_3 = 16 -6 = 10[/tex]

Notice the calculated differences in (2) are the same.

Hence, the table is a quadratic function

Answer:

I think you are right

Step-by-step explanation:

Answer:

Step-by-step explanation:

a, b, c

a + b > c ; b + c > a ; a + c > b

5 + 4 < 10 ⇒ triangle not possible

Answer:

Triangle not possible.

Step-by-step explanation:

The Triangle Inequality Theorem states that the sum of two sides must be larger than the third side.

5 + 4 = 9

9 cm is not longer than 10 cm.

10 > 9

Therefore, the triangle is not possible..

Given:

Consider the given statement is "7 more than the quotient of a number and 9 is 2".

To find:

The value of the unknown number.

Solution:

Let be the unknown number.

Quotient of a number and 9: [tex]\dfrac{x}{9}[/tex]

7 more than than the quotient of a number and 9: [tex]\dfrac{x}{9}+7[/tex]

It is given that, 7 more than the quotient of a number and 9 is 2.

[tex]\dfrac{x}{9}+7=2[/tex]

Multiply both sides by 9.

[tex]x+63=18[/tex]

[tex]x=18-63[/tex]

[tex]x=-45[/tex]

Therefore, the unknown number is -45.