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AURORKA [14]
3 years ago
13

Given △ABC≅△JKL, m∠B=55°, and m∠L=25°, what is the measure of ∠J?

Mathematics
2 answers:
8_murik_8 [283]3 years ago
6 0
For the answer to the question above, 
<span><J = 100
</span><span>because they are similar they have the same angles
</span>The two triangles are similar, so they must have corresponding angles. Thats one way to define similarity, it can dilate (zoom in /zoom out) , but the angles are preserved. You can also define similarity in terms of the proportionality of the sides. 

"Given △ABC≅△JKL"

The order of the letters counts. 
<A = <J
<B = <K
<C = <L

<span>now you can draw two generic triangles, which have the same three angles, but label the angles accordingly, so they match up.
</span>
<span>then by correspondance we can fill in
</span>nightowlthe third angle can be found by the fact that 
the three angles must add up to 180.
alexandr1967 [171]3 years ago
5 0

Answer:

100°

Step-by-step explanation:

Using the congruence statement, we know that ∠A≅∠J, ∠B≅∠K, and ∠C≅∠L.∠

Since m∠B = 55, then m∠K = 55.

Along with ∠L, this gives us 2 of the 3 angles of triangle ABC.  We know that the sum of the measures of the angles in a triangle is 180°; this means that

∠J = 180-(55+25) = 180-80 = 100°

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NeX [460]

Answer:

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The slope is m=-0.5.

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Step-by-step explanation:

Our aim is to calculate the values <em>m</em> (slope) and <em>b</em> (y-intercept) in the equation of a line :

y=mx+b

We have the following data:

\begin{array}{c|cccc}x&2&4&6&12\\y&11&10&9&6\end{array}

To find the line of best fit for the points given, you must:

Step 1: Find X\cdot Yand X\cdot X as it was done in the table below.

Step 2: Find the sum of every column:

\sum{X} = 24 ~,~ \sum{Y} = 36 ~,~ \sum{X \cdot Y} = 188 ~,~ \sum{X^2} = 200

Step 3: Use the following equations to find <em>b</em> and <em>m</em>:

\begin{aligned}        b &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} =             \frac{ 36 \cdot 200 - 24 \cdot 188}{ 4 \cdot 200 - 24^2} \approx 12 \\ \\m &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2}        = \frac{ 4 \cdot 188 - 24 \cdot 36 }{ 4 \cdot 200 - \left( 24 \right)^2} \approx -0.5\end{aligned}

Step 4: Assemble the equation of a line

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The graph of the regression line is:

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Answer:

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