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NeTakaya
2 years ago
15

In a rectangle, a diagonal forms a 36° angle with a side. Find the measure of the angle between the diagonals, which lies opposi

te to a shorter side.
Mathematics
1 answer:
bezimeni [28]2 years ago
8 0

Answer:

The answer is 72 degrees

Step-by-step explanation:

The picture that Helpmetnx showed does work. But they made a mistake and assumed that the diagonal is a angle bisector, and it's not.

1. rectangle ABCD, BD & AC are the diagonals. ∠ABD =36 degrees

2. ∠ABD= ∠BDC = 36 - alternate interior angles

3. ∠DBC = 90 - 36 = 54. ∠DBC =∠ADB = ∠BCA = 54

4. Now we know that the triangle formed between the two diagonals is a isosceles triangle because of base angle theorem.

5. 180 - 54*2 = 72 degrees

I hope this helps!

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One hundred teachers attended a seminar on mathematical problem solving. The attitudes of representative sample of 12 of the tea
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Answer:

a) 1.92

b) 3.25

c) 1.5

d) -5.23

Step-by-step explanation:

We are given the following in the question:

4, 7, -1, 1, 0, 5, -2, 2, -1, 6, 5, -3

a) mean of score change

Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}

Mean =\displaystyle\frac{23}{12} = 1.92

b) standard deviation for this population

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}  

where x_i are data points, \bar{x} is the mean and n is the number of observations.

Sum of squares of differences = 126.92

\sigma = \sqrt{\frac{126.92}{12}} = 3.25

c) median change score

Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}

Sorted data: -3, -2, -1, -1, 0, 1, 2, 4, 5, 5, 6, 7

Median =

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4 0
2 years ago
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We will take the volume of each box separately to find the difference between them.
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Answer:

Step-by-step explanation:

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4 0
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