# Explain how you can use the Triangle Sum Theorem to find the measures of the angles in an equilateral triangle.The angles of an equilateral triangle are . Let the measure of each angle be x. Then, by the Triangle Sum Theorem, x + x + x = 3x = °_____________. Solving for x gives x = °____________.

The first blank is 180

The second blank is 60

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The triangle sum theorem basically says that adding up all three angles of any triangle always leads to 180 degrees. So that's why

(angle1)+(angle2)+(angle3) = 180

x+x+x = 180

3x = 180

Divide both sides of that last equation by 3. This is to undo the multiplication of 3 done to x.

3x = 180

3x/3 = 180/3 ... divide both sides by 3

x = 60

Each angle of this equilateral triangle is 60 degrees. In an equilateral triangle, all three sides are the same length. Also in an equilateral triangle, all three angles are the same measure and always 60 degrees.

The Triangle Sum Theorem says that all angles in a triangle add up to 180 degrees. In an equilateral triangle, all angles are equal. Hence, each angle is 60 degrees.

### Explanation:

The Triangle Sum Theorem states that the sum of the measures of the angles in a triangle is always 180 degrees. Now, in an equilateral triangle, all angles are equal. Let's denote the measure of each angle with x. According to the theorem, the sum of these measures is x + x + x = 180. Simplifying this gives 3x = 180. Hence, solving for x, which refers to the measure of each angle in the equilateral triangle, we get x = 180 / 3 = 60 degrees. Thus, each angle in an equilateral triangle measures 60 degrees.

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## Related Questions

What is a simplified form of the expression 2(–x + 2) + 3x?

In the simplified form the expression is x+4

x+4

Step-by-step explanation:

At a certain car dealership, 20% of customers who bought a new vehicle bought an SUV, and 3% of them bought a black SUV (that is 3% of customers bought a vehicle that was an SUV and in black color). Given that a customer bought an SUV, what is the probability that it was black?

Step-by-step explanation:

As per given , the probability that customers who bought a new vehicle bought an SUV : P(SUV) = 0.20

The probability that customer bought a vehicle that was an SUV and in black color : P(SUV and black)  =0.03

Now by suing conditional probability formula,

If we have given that a customer bought an SUV, then the probability that it was black will be :

Hence, the required probability is 0.15.

The probability that a customer who bought an SUV also bought a black SUV is 0.006, or 0.6% (expressed as a percentage).

To find the probability that a customer who bought an SUV also bought a black SUV, you can use conditional probability.

Let's define the following events:

A: A customer bought an SUV.

B: A customer bought a black SUV.

You are given that P(B|A) is the probability that a customer who bought an SUV also bought a black SUV, which is 3% or 0.03.

You want to find P(B|A), the probability that a customer who bought an SUV also bought a black SUV. You can use the following formula for conditional probability:

P(B|A) = (P(A and B)) / P(A)

Here, P(A and B) is the probability that a customer bought both an SUV and a black SUV, and P(A) is the probability that a customer bought an SUV.

You know that P(B|A) = 0.03 and P(A) = 0.20.

Now, you need to find P(A and B), the probability that a customer bought both an SUV and a black SUV. You can rearrange the formula:

P(A and B) = P(B|A) * P(A)

P(A and B) = 0.03 * 0.20

P(A and B) = 0.006

for such more question on probability

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left bottem

Step-by-step explanation:

The 2nd one is correct

Step-by-step explanation:

Factorize each expression. (a) r² +2rt - 2st - rs​

so first split into two

now we can factorise each

now the inside of the bracket is the same so we can reconfigure like this

all i did was put the two outside terms together to make (r-s)

(r-s)(r+2t)

The value of x is given by the pythagoras theorem
X^2 = 17^2 - 15^2
X^2 = 289-225
X^2 = 64
X = sqrt64
X= 8cm

Suppose a regional computer center wants to evaluate the performance of its memory system. One measure of performance is the average time between failures of its disk drive. To estimate the value, the center recorded the time between failures for a random sample of 45 drive failures. The sample mean has been computed to be 1,762 hours and the sample standard deviation is 215. Estimate the true mean time between failures with a 90% confidence interval? Interpret the confidence interval.

The 90% confidence interval is (1408.325 hours, 2115.675 hours).

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

So it is z with a pvalue of , so

Now, find M as such

In which s is the standard deviation of the sample. So

The lower end of the interval is the mean subtracted by M. So it is 1762 - 353.675 = 1408.325 hours.

The upper end of the interval is the mean added to M. So it is 6.4 + 0.3944 = 2115.675 hours.

The 90% confidence interval is (1408.325 hours, 2115.675 hours).