1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
gladu [14]
3 years ago
15

Need help with this geometry question

Mathematics
1 answer:
yan [13]3 years ago
5 0

Answer:

UT = TW + WU = 27 + 27 = 54

WT = 27

ST = UT = 54

arc(XT) =  angle XZT = 52 degrees

arc(ST) = angle SZT = 104

arc(US) = arc(ST) + arc(UT) = 104 + 104 = 208

I know it was super drawn out and there were probably quicker ways to do it, but I was justusing methods that came to mind rather than going for efficiency.  let me know if any part is confusing.  

Step-by-step explanation:

Let's start by just building on what we know

Since we know sv and vz can be made into the side of two triangles, SZV and TZV, we can use some similar triangle rules.

In SZV and TZV we know SZ = TZ since they are both radii, ZV = ZV because they are the same line and angle ZVS = angle ZVT since they are supplementary and one is 90 degrees.  This allows us to solve and see if they are congruent or not.  To do so we use the normal trig functions

sin(ZTV) = ZV/ZT = ZV/12

sin(ZSV) = ZV/SV = ZV/12

So the angles could be equal, but just to be sure lets look at all possible answers.  with sine an angle x gives the same result as 180-x.  Since both angles are acute thugh we know this can't be true so both angles are equal.    Now we can say both triangles are congruent by AAS.  Since they are congruent we can then confirm SV = VT.

In general you can say if a radii intersects a chord at a right angle then the intersection is a bisection.  So now we know VT = 27

We can use similar methods to show UW = WT and if you made two triangles ZWT and ZWU you will see they are congruent.  and since arc UT is 104 degrees that means angle UZT is 104 degrees.  Since ZW bisects UT and the two triangles are congruent ZW also bisects angle UZT so UZW = TZW = 52 degrees.

Now we have 4 triangles, SZV, TZV, ZWT and ZWU and we know SZV and TZV are congruent and ZWT and ZWU are congruent.  Now, if we can make one from each pair congruent we would knwo all four are congruent.  Since TZV and ZWT share a side  that's a good place to start.  Looking at these two  triangles we know those two sides are equal, and they both have a right angle.  Also we know VZ = ZW fromt he instructions, so this is again a chance to check with trig.

Let's look at angle ZTW and ZTV.

sin(ZTW) = ZW/ZT = 27/ZT

sin(ZTV) = VZ/ZT = 27/ZT

Using the same reasoning as before we can say that the two angles are equal, so the two triangles are congruent.  Now we can say a lot.

angle UZT = angle SZT = 104 degrees

angle SZV = angle VZT = angle TZW = angle WZU = 52

SV = VT = TW = WU = 27

Let's start solving.

UT = TW + WU = 27 + 27 = 54

WT = 27

ST = UT = 54

arc(XT) =  angle XZT = 52 degrees

arc(ST) = angle SZT = 104

arc(US) = arc(ST) + arc(UT) = 104 + 104 = 208

You might be interested in
The population of China is 1,352,600,000 and the US is 327,200,000. How many more people are living in China than the US.
777dan777 [17]

Answer:

1,025,400,000

Step-by-step explanation:

I hope this helped!

5 0
2 years ago
Evaluate the expression when m = 6 and n<br> 8.<br> 56<br> +m<br> n
Marina86 [1]

Step-by-step explanation:

Hello! I have given you the answer key to your whole entire unit, so what you do is scroll to find the answer you need out of it. But if it isn't on the front like it should be, scroll you'll find it.

Download pdf
8 0
3 years ago
Read 2 more answers
How is the graph of the parent function?
Grace [21]

Answer:

because the parent is the top graph which means the parent is greater

Step-by-step explanation:

3 0
3 years ago
Quadrilateral PQRS is transformed by translating it 6 units to the right and then rotating it 90° clockwise
Elina [12.6K]

Answer:

(y, -x -6)

Step-by-step explanation:

<em>The coordinates of PQRS is not given, however we'll assume the coordinates of PQRS to be (x,y)</em>

<em />

The first transformation: 6 units right

(x,y) -> (x + b, y)

Where b = 6

So, the new coordinates will be

(x + 6, y)

The second transformation: 90° clockwise

(x,y) -> (y,-x)

So, the new coordinates will be

(x + 6, y)-> (y, -x -6)

<em>Hence, the new coordinates of PQRS is (y, -x - 6)</em>

7 0
3 years ago
Hey! I need loads of help on this! If you could help it would be such a relief!
il63 [147K]

Answer 1: For the Parallelogram inside the rectangle the area = 48

Rectangle = 275     275+48 = 323

Answer 2: For the answer for the square inside the parallelogram = 36

The answer to the parallelogram = 120     120+36 = 156

Step-by-step explanation: #1: A = bh = 12 · 4 = 48

A = wl = 11 · 25 = 275

#2: A = a2 = 62 = 36

A = bh = 15 · 8 = 120

Sorry if u didn't have to add im not to good at this ;(

Hope that helped though!

4 0
3 years ago
Other questions:
  • Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well
    13·1 answer
  • If a company has five employees with annual salaries of $60,000, $70,000, $60,000, $90,000, and $80,000, respectively, what is t
    8·1 answer
  • Arrange these numbers from least to greatest -5 positive 3 negative 2 1​
    13·2 answers
  • A teacher decides to purchase a new car and considers two options. Option one is the new Zoomba for $60,000 with an expected dep
    12·1 answer
  • Sinead bought 2 shirts for $15.95 each and a pair of shoes for $42.14. If she paid for the items with a $100 bill, how much chan
    10·1 answer
  • 24 POINTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    5·1 answer
  • Please help me!! I will mark brainliest
    8·1 answer
  • What is the sum of 1.57 and 6.88?
    14·2 answers
  • What is the distance between A(5, 4) and<br> B(2, -3)?
    12·2 answers
  • Please help me with this
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!