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Colt1911 [192]

Answer:

angle list = measure
2, 4 = 35°
3, 7, 9 = 52°
11 = 87°
1, 5, 10, 12 = 93°
6, 8 = 128°

Step-by-step explanation:

As with a lot of math, it helps to understand the vocabulary. That helps you understand what is being said when the words are used to form a thought.

A "transversal" is a line that cuts across two parallel lines. At each intersection, 4 angles are formed. The angles are given different names, so we can talk about pairs of them being congruent.

The four angles between the parallel lines are called interior angles. The four angles outside the parallel lines are called exterior angles. When the angles are on opposite sides of the transversal, they are alternate angles.

In the diagram, we can identify the following pairs in each category:

alternate interior: {3, 9}, {5, 10}
alternate exterior: {1, 12}, {7, 52°}

When interior angles are on the same side of the transversal, they are called same-side or consecutive interior angles. Exterior angles cannot be consecutive. Here are some in that category:

consecutive interior: {3, 6}, {5, 87°}

Angles created by a ray extending from a line are a linear pair. Angles of a linear pair are supplementary, that is, their sum is 180°. Angles formed by two intersecting lines, sharing only the same vertex, are called vertical angles. Vertical angles are both supplementary to the other angle of the linear pair of which they are a part. Since they are supplementary to the same angle, they are congruent (have the same measure). Here are some linear pairs and some vertical angles in the figure:

linear pairs: {6, 7}, {7, 8}, {8, 9}, {6, 9}, {10, 87°}, {10, 11}, {11, 12}, {12, 87°}
vertical angles: {1, 5}, {2, 4}, {3, 52°}, {6, 8}, {7, 9}, {10, 12}, {11, 87°}

Corresponding angles are ones that are in the same direction from the point of intersection. Some of those pairs are ...

corresponding angles: {1, 10}, {5, 12}, {3, 7}, {9, 52°}

Here are the relations that help you work this problem:

alternate interior angles are congruent
alternate exterior angles are congruent
vertical angles are congruent
corresponding angles are congruent
a linear pair is supplementary
consecutive interior angles are supplementary

__

So far, we haven't mentioned much about the angles where lines j, k, l all meet. Transversal j cuts some of the angles created by transversal k, and vice versa. So, there are some angle sum relations that also apply to corresponding angles:

∠1+∠2≅∠6
∠2+52°≅87°
∠3+∠4≅∠11
∠4+∠5≅∠8

_____

With an awareness of all of the above, you can figure the measures of all of the angles in the diagram.

∠1 ≅ ∠5 ≅ ∠10 ≅ ∠12 = 180° -87° = 93°

∠2+52° = 87° ⇒ ∠2 ≅ ∠4 = 87° -52° = 35°

∠3 ≅ ∠7 ≅ ∠9 ≅ 52°

∠6 ≅ ∠8 = 180° -∠7 = 128°

∠11 ≅ 87°

5 0

3 years ago

Help me answer this please dont take the point

aleksklad [387]

Answer:

ayo ur school name is out here lol

Step-by-step explanation:

4 0

3 years ago

A rectangular painting with a length of 54 cm has an area of 2052 cm² what is the width of the painting

garri49 [273]

$\huge \bold{ \mathfrak{ \red{Question} }}$

A rectangular painting with a length of 54 cm has an area of 2052 cm² what is the width of the painting .

$\huge {\bold {\mathfrak \red{Solution}}}$

$\mathsf{length = 54cm} \\ \mathsf{area = 2052} \\ \mathsf{breadth = x} \\ area = 2052 \\ l \times b = 2052 \\ 54 \times x = 2052 \\ x = \frac{2052}{54} \\ \boxed{x = 38cm}$

3 0

3 years ago

A researcher was interested in seeing how many names a class of 38 students could remember after playing a name game After playi

Andreas93 [3]

Answer:

Proportion of the students recalled more than 15 names is 91.77%.

Step-by-step explanation:

We are given that a researcher was interested in seeing how many names a class of 38 students could remember after playing a name game After playing the name game, the students were asked to recall as many first names of fellow students as possible.

The mean number of names recalled was 19.41 with a standard deviation of 3.17.

Let X = number of names recalled

SO, X ~ N( $\mu = 19.41,\sigma^{2} = 3.17^{2}$ )

The z-score probability distribution is given by ;

Z = $\frac{X-\mu}{\sigma} } }$ ~ N(0,1)

where, $\mu$ = mean number of names recalled = 19.41

$\sigma$ = standard deviation = 3.17

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, proportion of the students recalled more than 15 names is given by = P(X > 15 names)

P(X > 15) = P( $\frac{X-\mu}{{\sigma} } }$ > $\frac{15-19.41}{3.17} }$ ) = P(Z > -1.39)

= P(Z < 1.39) = 0.9177 {using z table}

Therefore, proportion of the students recalled more than 15 names is 91.77%.

4 0

3 years ago

Consider the following sample data for two variables. x y 7 7 8 5 5 9 3 7 9 7 Calculate the sample covariance. b. Calculate the

Semmy [17]

Answer:

a) Sample co-variance = -1.5

b) Sample correlation = -0.4404152

c) Weak negative relationship between X and Y.

Step-by-step explanation:

a) by sample co-variance = sum ((x - xbar)* (y-ybar)/n-1

#.... use the following program in R

x = c(7,8, 5, 3, 9)

y = c(7,5,9,7,7)

sv = sum((x-mean(x))*(y-mean(y)))/4

cor(x,y)

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4 0

3 years ago