All categories

2 years ago

If m∠2 = 41°, m∠5 = 94°, and m∠10 = 109°, find each measure.

Mathematics

1 answer:

Orlov [11]2 years ago

8 0

Answer:

Step-by-step explanation:

It's given in this question,

m∠2 = 41°, m∠5 = 94° and m∠10 = 109°

Since, ∠2 ≅ ∠9 [Alternate interior angles]

m∠2 = m∠9 = 41°

m∠8 + m∠9 + m∠10 = 180° [Sum of angles at a point of a line]

m∠8 + 41 + 109 = 180

m∠8 = 180 - 150

m∠8 = 30°

Since, m∠2 + m∠7 + m∠8 = 180° [Sum of interior angles of a triangle]

41 + m∠7 + 30 = 180

m∠7 = 180 - 71

m∠7 = 109°

m∠6 + m∠7 = 180° [linear pair of angles]

m∠6 + 109 = 180

m∠6 = 180 - 109

= 71°

Since m∠5 + m∠4 = 180° [linear pair of angles]

m∠4 + 94 = 180

m∠4 = 180 - 94

m∠4 = 86°

Since, m∠4 + m∠3 + m∠9 = 180° [Sum of interior angles of a triangle]

86 + m∠3 + 41 = 180

m∠3 = 180 - 127

m∠3 = 53°

m∠1 + m∠2 + m∠3 = 180° [Angles on a point of a line]

m∠1 + 41 + 53 = 180

m∠1 = 180 - 94

m∠1 = 86°

You might be interested in

A real estate agent wants to predict the selling price of single-family homes from the size of each house. A scatterplot created

kolezko [41]

Answer:

$\text{Selling price} = \$1000e^{5.6}$

The selling price of house is approximately 270.4264 thousand dollars.

Step-by-step explanation:

We are given the following in the question:

A linear model gives the relation between natural logarithm of price, in thousands of dollars, and size, in 100 square feet.

$\ln( \text{price})=2.08+0.11(\text{size})$

Let p be the price and s be the size.

$\ln(p) = 2.08 + 0.11(s)$

We have to approximate the selling price for a house with a size of 3,200 square feet.

Thus, we put s = 32

$\ln(p) = 2.08 + 0.11(32)\\\ln(p) = 5.6\\p = e^{5.6}\\p = 270.4264\\\text{Selling price} = \$1000e^{5.6}$

Thus, the selling price of house is approximately 270.4264 thousand dollars.

6 0

2 years ago

Substituting the equation y = 4x + 1 into the equation 2y = -x – 1 will produce the equation ________.

Zarrin [17]

Answer:

Step-by-step explanation:

Substituting y = 4x+1 into 2y = -x-1 gives the equation

2(4x+1) = -x-1

Solve the equation:

8x+2 = -x-1

9x = -3

x = -⅓

7 0

1 year ago

Read 2 more answers

Caroline bought 20 shares of stock at 10 ½, and after 10 months the value of the stocks was 11 ¼. If Caroline were to sell all h

OleMash [197]

20 shares at 10 1/2 (or 10.5) = 20 * 10.5 = 210
20 shares at 11 1/4 (or 11.25) = 20 * 11.25 = 225

so the profit made would be : 225 - 210 = $ 15 <==

4 0

1 year ago

Player V and Player M have competed against each other many times. Historical data show that each player is equally likely to wi

Helen [10]

Answer:

0.46 (46%)

Step-by-step explanation:

We have the following data:

- Probability that player V wins the first set:

$p(1)=0.50$

(because the text says the two players are equally likely to win the first set)

- Probability that player V wins the 2nd set if he has won the 1st set:

$p(2|1)=0.60$

So, the probability that player V wins the first 2 sets is:

$p(12)=p(1)\cdot p(2|1)=(0.50)(0.60)=0.30$ (1)

Instead, the probability that player V loses the 2nd set if he has won the 1st set is 0.40 (=1-0.60), so

$p(2^c|1)=0.40$

So, the probabiity that player V winse the 1st set but loses the 2nd set is

$p(12^c)=p(1)\cdot p(2^c|1)=(0.50)(0.40)=0.20$ (2)

Also, we have:

- Probability that player V loses the 1st set:

$p(1^c)=0.50$

- Probability that she will lose the 2nd set in this case is 0.70, it means that the probability that she will win the 2nd set if she lost the 1st set is 0.30, so:

$p(2|1^c)=0.30$

So, the probability that she will lose the 1st set and win the 2nd set is:

$p(1^c2)=p(1^c)\cdot p(2|1^c)=(0.50)(0.30)=0.15$ (3)

Combined together (2) and (3), this means that the probability that player V wins exactly 1 set out of the first two sets is:

$p(1/2)=p(12^c)+p(1^c2)=0.20+0.15=0.35$ (4)

At this point, the probability that she will win the 3rd set is

$p(3)=0.45$

This means that the overall probability that she will win the 3rd set if she won exacty 1 of the first 2 sets is:

$p(1/2,3) = p(1/2)\cdot p(3)=(0.35)(0.45)=0.16$ (5)

So, the overall probability that player V will win a match against player M is the sum of (1) and (5):

$p(W)=p(12)+p(1/2,3)=0.30+0.16=0.46$

5 0

2 years ago

Kyle challenges you to a game. Each player rolls a standard number cube twice. If the sum of the results is divisible by 3, you

sweet [91]

Answer:

The probability of you winning is 1/3

No, it is not a fair game

Step-by-step explanation:

The first thing we need to have here is the sample space. This refers to the set of all possible results that can occur from the rolling.

Please check attachment for this

Kindly note that the total number of possible outcomes is 36.

And in the attachment, sums which are divisible by 3 are circled.

The number of circles we can count is 12

Thus, the probability of you winning would be number of circles/total number of outcomes = 12/36 = 1/3

Is it a fair game?

No, it is not

It can only be a fair game if the probability of winning equals probability of losing ( which is 18/36 = 1/2 or 0.5)

8 0

2 years ago