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3 years ago

Find the values of x and y that make the quadrilateral a parallelogram

Mathematics

1 answer:

lana66690 [7]3 years ago

6 0

For given parallelogram, the value of x = 114° and y = 66°

<h3>Explanation: </h3>

<em>(Refer figure)</em>

Given quadrilateral ABCD is a parallelogram.

m∠A = 66°

m∠B = x°

m∠C = y°

m∠D = 114°

Since by properties of parallelogram, the both pairs of opposite sides of a parallelogram are parallel.

Opposite angles of a parallelogram are congruent ...........................(1)

Consecutive angles of a parallelogram are supplementary ................(2)

Using (1) for given parallelogram ABCD; we get,

m∠B = m∠D

m∠A = m∠C

Therefore x = 114° and y = 66°.

Using (2) to check whether the two consecutive angles are supplementary.

( m∠A + m∠D ) = ( m∠B + m∠C ) = ( m∠C + m∠D ) = 66° + 114° = 180°

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Step-by-step explanation:

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3 years ago

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3 years ago

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The heights, in inches, of the starting five players on a college basketball team are 6868, 7373, 7777, 7575, and 8484. Co

LenKa [72]

Answer:

The sample standard deviation of 5.95.9 inches differs from the population standard deviation of 5.25.2 inches because of their formulas for calculating it.

Step-by-step explanation:

We are given the heights, in inches, of the starting five players on a college basketball team ;

68, 73, 77, 75 and 84

Now whether we treat this data as sample data or population data, the mean height would remain same in both case because the formula for calculating mean is given by ;

Mean = Sum of all data values ÷ No. of observations

Mean = ( 68 + 73 + 77 + 75 + 84 ) ÷ 5 = 75.4 inches

So, numerically, the sample mean of 75.4 inches is the same as the population mean.

Now, coming to standard deviation there will be difference in both sample and population standard deviation and that difference occurs due to their formulas;

Formula for sample standard deviation = $\frac{\sum (X_i - Xbar)^{2} }{n-1}$

where, $X_i$ = each data value

X bar = Mean of data

n = no. of observations

Sample standard deviation = $\frac{ (68 - 75.4)^{2} +(73 - 75.4)^{2}+(77- 75.4)^{2}+(75- 75.4)^{2}+(84 - 75.4)^{2} }{5-1}$

= 5.9 inches

Whereas, Population standard deviation = $\frac{\sum (X_i - Xbar)^{2} }{n}$

= $\frac{ (68 - 75.4)^{2} +(73 - 75.4)^{2}+(77- 75.4)^{2}+(75- 75.4)^{2}+(84 - 75.4)^{2} }{5}$ = 5.2 inches .

So, that's why sample standard deviation of 5.95.9 inches differs from the population standard deviation of 5.25.2 inches only because of formula.

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3 years ago

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sladkih [1.3K]

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Step-by-step explanation:

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