In triangle XYZ, XY¯¯¯¯¯¯¯¯=15, YZ¯¯¯¯¯¯¯=8, ∡X=(3w−35)°, and ∡Y=52°. In triangle RST, RS¯¯¯¯¯¯¯=15, RT¯¯¯¯¯¯¯=8, ∡R=(w+17)°, and ∡S=52°. Find the angle measure for each of the four angles whose measures are not known.



A. ∡R=43°, ∡T=85°, ∡X=43°, ∡Z=85°


B. ∡R=64°, ∡T=64°, ∡X=64°, ∡Z=64°


C. ∡R=35°, ∡T=93°, ∡X=35°, ∡Z=93°


D. ∡R=52°, ∡T=76°, ∡X=52°, ∡Z=76°

Answers

Answer 1

Answer:

A. ∡R=43°, ∡T=85°, ∡X=43°, ∡Z=85°

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. The types of triangles are scalene triangle, equilateral triangle, right angled triangle and obtuse triangle.

Cosine rule states that given a triangle with sides a, b, c and their corresponding angles opposite to the sides as A, B, C. Then:

[tex]a^2=b^2+c^2-2bc*cos(A)[/tex]

In triangle XYZ, we can find XZ using cosine rule:

[tex]XZ^2=XY^2+YZ^2-2(XY)(YZ)cosY\\\\subtituting:\\\\XZ^2=15^2+8^2-2(15)(8)cos(52)\\\\XZ^2=141.24\\\\XZ=11.88\\\\Using\ sine\ rule:\\\\\frac{XZ}{sin(Y)}=\frac{XY}{sin(Z)}\\\\\frac{11.88}{sin(52)}=\frac{15}{sin(Z)}\\\\sin(Z)=15*sin(52) /11.88\\\\sin(Z)=0.9946\\\\Z=sin^{-1}(0.9946)\\\\Z=85^0[/tex]

∠X + ∠Y + ∠Z = 180° (sum of angles in a triangle)

∠X + 52 + 85 = 180

∠X + 137 = 180

∠X = 43°

∠X = 3w - 35

3w - 35 = 43

3w = 78

w = 26

In triangle RST, using sine rule:

∠R = w + 17

∠R = 26 + 17

∠R = 43°

∠R + ∠S + ∠T = 180° (sum of angles in a triangle)

43 + 52 + ∠T = 180

∠T + 95 = 180

∠T = 85°


Related Questions

The propability of Sachin's team winning any match is 0.45

Write down the propability of sachin's team not winning any match.

Answers

Answer:

0.55

Step-by-step explanation:

o.45 + X = 0.55

the probability of not winning is 0.55

An athletics club has junior
(i.e. boy or girl) members and adult members.
The ratio of girls to boys to adults is 3:4:9
and there are 16 more adult members than
junior members. In total, how many members
does the club have

Answers

Answer:

The total number of members are 128 members

Step-by-step explanation:

From the question, mixing the ratio of children to adult, we have ;

7:9

There are 16 more adult members

So if there are x children, then there are 16 + x adults

Thus, the total number of members will be;

16 + x + x = 2x + 16

Now, we have that;

7/16 * (2x + 16) = x

7(2x + 16) = 16x

14x + 112 = 16x

16x-14x = 112

2x = 112

x = 112/2

x = 56

The total number of members is thus;

2(56) + 16 = 128

PLS HELP I'LL MARK BRAINLEST

Answers

Answer:

a

Step-by-step explanation:

180-50

Hey there!

Hope this helps!

x=130

Re write the statement 19+7 divided by 2-5 by including one pair of brackets to make the total equal to 8

Answers

[19+7]/2-5

19+7=26
26/2=13
13-5=8

Which of the following graphs represents the equation y- 4 =3(x-1)
A. Graph A.
B. Graph B
C. Graph
D. Graph D
please help

Answers

Answer:D

Step-by-step explanation:y-4=3(x-1)

y-4=0 3(x-1)

y=-4 , 3x-3

y=-4=3x-3

3 3

y=-4, = x=1

y-x=1+4=5

The answer is graph D

Gift boxes at Walgreens are sold in packs of 8, and cost $6.00. At CVS, the price for a 10 pack of gift boxes is $9.00. Determine which store offers a better bargain based on the price per box. Type the name of the store on the line.

Answers

Answer:

CVS

Step-by-step explanation:

i am pretty sure

The price of gas was $2.49 last month. This month, gas costs $2.79. What is
the percent increase?

Answers

2.79 - 2.49 = .30

then divide the amount increased by the original number and multiply by 100

.3 / 2.49 x 100 = 12%

Answer:

12%

Step-by-step explanation:

2.79 - 2.49 = $0.30

0.30 / 2.49 = 0.12 = 12% (decimal changes to percent)

You can check your work by doing original cost times the decimal of the percent increase. $2.49 * 0.12 = $0.30. Add this to original -> 0.30 + 2.49 = $2.79.  

This trapezoid based right pyramid has a volume of 48m cubed with a height of 8 and slant height of 14 what is the area of the base of the pyramid

Answers

Answer:

18

Step-by-step explanation:

Khan Academy

Geometry- which statement is true

Answers

Answer:

its the 3rd one ab and cd

Select all the inequalities that relate the sides of the figure shown.

b
c>a

c
b>a

a

Answers

Answer:

b

Step-by-step explanation:

According to the given angles in the question, angle b is greater than angle a.

What is inequality?

Mathematical equations with inequalities on both sides are known as inequalities. In an inequality, we compare these two values as opposed to equations. Somewhere between, the equal sign is changed to a less than (or less than or similar to), bigger than (or greater or equal to), or just not equal to sign.

As per the given data from the question,

The side which has got a larger angle has the largest side.

The side c is greater than a and side b is also greater than a.

The remaining angle can be calculated as:

The sum of all angles will be equal to 360.

x + 75 + 90 + 105 = 360

x = 90°.

To know more about inequality:

https://brainly.com/question/20383699

#SPJ2

14 is 33 1/2% of what number?

Answers

Answer:

41.79

Step-by-step explanation:

c = 14 * 100/33.5 = 1400/33.5 = 2800/67

= 41.79104

at a concession stand three hotdogs in for hamburgers cost $13.50 for hotdogs and three hamburgers cost $12.75 find the cost of one hotdog and find the cost of one hamburger

Answers

Price of Hotdogs you do 14.50/3= 4.50
Price of Hamburgers 12.75/3=4.25

What is the image of the point (3,2)(3,2) after a rotation of 90^{\circ}90 ∘ counterclockwise about the origin?

Answers

Answer: = (-2,3)

Step-by-step explanation:

Rotation is a transformation of a figure by rotating it for a specific angle about a fixed point.

Here, fixed point = origin = (0,0)

Transformation rule for rotation of  [tex]90^{\circ}[/tex]counterclockwise about the origin:

[tex](x,y)\to (-y,x)[/tex]

Then, the image of the point (3,2) =  (-2,3)

Hence, the image of the point (3,2) after a rotation of  [tex]90^{\circ}[/tex]counterclockwise about the origin = (-2,3)

Answer: The answer is -2,3 because 90 degrees of the orgin :) enjoy

Step-by-step explanation:

32% of 25 is what number

Answers

Answer:

8

Step-by-step explanation:

it just is

Answer:

8

Step-by-step explanation:

Convert to a decimal

32%

move two decimal points to the left

0.32

multiply

0.32 times 25 = 8

Max is flying a kite and gets tired of holding the string attached to the kite. Max has let out approximately 40 feet of string and the string makes a 32 degree angle with the ground. How high is the kite at the time?

Answers

Answer: i think 8

Step-by-step explanation:

4y=x+8 pls answer hurry up pls

Answers

Answer:

x=-8

y=2

Step-by-step explanation:

Would love it if you guys helped me and showed solutions! Brainly points and thank you points too! <3
Unitary method question.

Answers

Answer:

the better value is £9

Step-by-step explanation:

unitary method..

find out how much 1kg will cost in the supermarket and multiply by 12.5kg

For the supermarket

1.83/2.5= 0.732 for one kg.

for 12.5 kg

0.732× 12.5= £9.15

hence the farm shop price is lower than the supermarket price

How many times will the graph of this equation cross the x-
axis?
y= 22^2– 7x - 9

Answers

I’m not sure but I hope yu get the right help

which letter would be the most meaningful variable for this problem situation? the distance a bike travels divided by 3!

Answers

Answer:

We could use 'd' as a variable to represent distance. And since distance is the most important thing in this question, the most important variable would be 'd'.

Is this what you were asking?

I hope I could help. (๑•~•)

Please help with this question

Answers

Answer:

-16

Step-by-step explanation:

becjv dfv igcicifcigxixixicocvicicirxc ou9 xexiixi xiexexuwuzwxit

Answer:

I would say  57 is the answer

Step-by-step explanation:

What is the largest integer that makes 4t - 42 - 18t > -14 true?​

Answers

Answer:

[tex]t < - 2 \\ t = - 3[/tex]

Step-by-step explanation:

[tex]4t - 42 - 18t > - 14[/tex]

[tex]4t - 18t > - 14 + 42[/tex]

[tex] - 14t > 28[/tex]

[tex] \frac{ - 14t}{ - 14} < \frac{28}{ - 14} [/tex]

[tex]t < - 2[/tex]

[tex]if \: \: \: \: \: t = - 3[/tex]

[tex]4t - 42 - 18t { > }^{?} - 14[/tex]

[tex]4 \times - 3 - 42 - 18 \times - 3 { > }^{?} - 14[/tex]

[tex] - 12.6 > - 14[/tex]

Can someone help me ?

Answers

Answer:

Step-by-step explanation:

Given

let the unknown angle be x then,

with reference angle x

perpendicular(p) = 3

base(b)= 9

now

tan x = p/b

tan x = 3 / 9

tan x = 1 / 3

x = tan ^-1( 1/3)

x = 18.43°

hope it will help u :)

PLEASE HELPPPPP!!!
There is a line that includes the point (–4, 2) and has a slope of 1/4 .What is its equation in slope-intercept form?

Answers

Step-by-step explanation:

Slope-intercept form: y = mx + c

We have m = 1/4. Since it passes through the

point (-4, 2), => When x = -4, y = 2.

=> (2) = (1/4)(-4) + c, 2 = c - 1, c = 3.

Hence the equation is y = x/4 + 3.

Answer:

Y = 1/4x + 3

Step-by-step explanation:

John bought 4 pants that each cost the same amount and a pair of sneakers that cost $65. The items he bought cost a total of $145 before tax was added. Which equation represents the cost of each pants, p.

Answers

Answer:p=$20

Step-by-step explanation:

145-65=80

80/4=20

so each pant costs $20

p=$20

3/5 is simplest form yes or no

Answers

Answer:

Yes

Step-by-step explanation:

3 and 5 don't got a GCF

PLEASE HELP if 5 more than 3 times a number is -4, what is the number?

Answers

Answer:

x = -3

hope it's helpful ❤❤❤

THANK YOU.

Hey there!

The answer to your question is "n = -3"

First, we can start by writing the equation as it says. "3 times a number" represents a number times 3, or "3n"

3n

Next, "5 more" represents addition, so "+ 5"

3n + 5

Finally, "is -4" means it is equal to -4, so "= -4"

3n + 5 = -4

Now that we have our equation, we can solve:

3n + 5 = -4

First, we subtract "5" from both sides of the equal sign:

3n = -9

Lastly, we divide both sides by "3".

n = -3

Have a terrificly amazing day!

The volume of a cube is 96 cubic millimeters. What is the length of each edge of the cube?

Answers

Answer:

V= a³ => 96 = a³ => a= ∛96 =2∛12

The length of each edge of the cube : C : 2∛12

Step-by-step explanation:

What is the slope of the line?

Answers

5/8 nxnznsn Josh’s said McManus McDonald’s 789 week

2/3

i dont know how to explain it all i learned was rise over run (rise/run) just like y/x but its easier to rmrmber

Find the coordinates of the point on the directed segment from (1,2) to (6,12) that divides it into a ratio of 2:3

Answers

Answer:

Point of contact  ( 3,6)

Step-by-step explanation:

Step(i):-

Given that the points are (1,2) and (6,12)

The ratio 2:3 divides the line segment

The line segment divides m:n externally

[tex](\frac{mx_{2}-nx_{1} }{m-n} ,\frac{mx_{2}-nx_{1} }{m-n} )[/tex]

Step(ii):-

(x₁, y₁) = (1,2) and (x₂, y₂)= (6,12) and m:n =2:3

[tex](\frac{2(6)+3(1) }{2+3} ,\frac{2(12)+3(2) }{2+3} )[/tex]

([tex](\frac{12+3}{5} ,\frac{24+6}{5} )[/tex]

([tex]\frac{15}{5} ,\frac{30}{5})[/tex]

(3 , 6)

Final answer:-

Point of contact  ( 3,6)

Help me with this circle question

Answers

Answer:

50.265482457436 inches

Step-by-step explanation:

radius = 8 inches

C = 2×pi×r

= 2×pi×8

C = 50.265482457436 inches

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