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2 years ago

If p is parallel to q, which pair of angles must be congruent?

Mathematics

2 answers:

Veseljchak [2.6K]2 years ago

5 0

Vertical angles are congruent whether the lines are parallel or not.
Corresponding angles are congruent.
Alternate interior and alternate exterior angles are congruent.
1 & 4, 2 & 3, 3 & 6, 4 & 5, 1 & 8, 2 & 7, 5 & 8, 6 & 7, 3 & 7, 1 & 5, 2 & 6, 4 & 8
I think I got all of them!

yuradex [85]2 years ago

4 0

When two lines are parallel and are intersected by a third line,

Then the pairs of corresponding angles are congruent.

The pairs of Alternate interior angles are congruent.

More names can be given to these angles.

But when we consider all corresponding and alternate angles, all angles are covered.

In the given figure

<2 = <6, <4 = <8, <1 = <5 and <3= <7 are all corresponding angles. ..(1)

Also < 4 = <5 & <3 = <6 are alternate interior angles. ...(2)

If we compare Statement (1) & statement (2)

We get

<1 = <5 = <8 = <4

<3 = <7 = <6 = <2

So all red dotted angles are equal

Also all black dotted angles are equal.

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What is the GCF of 35,42,38

lbvjy [14]

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2 years ago

I am completely lost and I need help to understand

garik1379 [7]

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2 years ago

Please help! I don't understand how to solve this problem

Ilia_Sergeevich [38]

Using the z-distribution, a sample of 142,282 should be taken, which is not practical as it is too large of a sample.

<h3>What is a z-distribution confidence interval?</h3>

The confidence interval is:

$\overline{x} \pm z\frac{\sigma}{\sqrt{n}}$

The margin of error is:

$M = z\frac{\sigma}{\sqrt{n}}$

In which:

$\overline{x}$ is the sample mean.

z is the critical value.

n is the sample size.

$\sigma$ is the standard deviation for the population.

Assuming an uniform distribution, the standard deviation is given by:

$S = \sqrt{\frac{(4 - 0)^2}{12}} = 1.1547$

In this problem, we have a 95% confidence level, hence $\alpha = 0.95$ , z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$ , so the critical value is z = 1.96.