Sean asked 10 of his classmates the amount of their weekly allowance. He recorded the information in this table

Match the following items.

Margarita [4]

Answer:

$1. m\angle ECB=50\\2. m\textrm{ arc BC}=100\\3. m\textrm{ arc CD}=80\\4. m\angle DCF=40$

Step-by-step explanation:

Given:

$\angle DBC=40$ °

From the triangle, using the theorem that center angle by an arc is twice the angle it subtend at the circumference.

$m\textrm{ arc CD}=2\times \angle DBC\\m\textrm{ arc CD}=2\times 40=80$

Also, the diameter of the circle is BD. As per the theorem that says that angle subtended by the diameter at the circumference is always 90°,

$m\angle BCD=90$

From the Δ BCD, which is a right angled triangle,

$m\angle DBC+m\angle BDC=90\textrm{ (right angled triangle)}\\40+m\angle BDC=90\\m\angle BDC=90-40=50$

Now, using the theorem that angle between the tangent and a chord is equal to the angle subtended by the same chord at the circumference.

Here, chords CD and BC subtend angles 40 and 50 at the circumference as shown in the diagram by angles $m\angle DBC\textrm{ and }m\angle BDC$ and EF is a tangent to the circle at point C.

Therefore, $m\angle DCF=m\angle DBC=40\\m\angle ECB=m\angle BDC=50$

Again, using the same theorem as above,

$m\angle DCF=50\\\therefore m\textrm{ arc BC}=2\times m\angle DCF=2\times 50=100$

Hence, all the angles are as follows:

$1. m\angle ECB=50\\2. m\textrm{ arc BC}=100\\3. m\textrm{ arc CD}=80\\4. m\angle DCF=40$

6 0

2 years ago

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Elly's room measures 78 inches by 96 inches. Sarah's room measures 66 inches by 108 inches. They want to combine their rooms. Ho

frozen [14]

Okay add 78 and 66. Then add 96 and 108. It should be 144 by 204. I know math is hard, but when you work at it you can do amazing things! I hope that helps you.

7 0

2 years ago

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The ratios in an equivalent ratio table are 3:12, 4:16, and 5:20. If the first number in theratio is 10, what is the Second numb

Zanzabum

Answer:

10:40

Step-by-step explanation:

As the left number increases by 1, the right number increases by 4. So as you can see, the left numbers go 3-4-5 while the right numbers go 12-16-20. So the answer is 10:40 because 10x4=40.

6 0

2 years ago

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You buy a new television for $3,100. The value of the television decreases by 12 percent every year. How much is the television

IrinaK [193]

Answer:

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