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3 years ago

Given the diagram of parallelogram LMNO, solve for r.

Mathematics

2 answers:

goldfiish [28.3K]3 years ago

5 0

So here is how we are going to solve for r. In a parallelogram, given angles L and N are equal in measure, as well as angles M and O. Angles L and O are supplementary angles, as well as M and N. So the first thing we are going to do is to solve for t first.
3t-15=2t+10
3t-2t=10+15
t=25
Angle O : 2t + 10
2(25)+10 = 60
Adding L and O together gives you 180
so 4r+60=180
4r=120
r=30
And 30*4=120
So r = 30
and angle L = 120
Hope this answers your question.

Maslowich3 years ago

3 0

I got 30. If you set M and I equal to each other and solve you get 25. If you substitute 25 for t you get 60. L and I should be supplementary so if you subtract 60 from 180 you get 120. Lastly, since you're solving for r, you need to divided 120 by 4 to get 30.

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April worked 1 1/2 times as long on her math project as did Carl. Debbie worked 1 1/4 times as long as Sonia. Richard worked 1 3

vlada-n [284]

Answer:

Student Hours worked

April. $7\frac{7}{8} \ hrs$

Debbie. $8\frac{1}{8}\ hrs$

Richard. $7\frac{19}{24}\ hrs$

Step-by-step explanation:

Some data's were missing so we have attached the complete information in the attachment.

Given:

Number of Hours Carl worked on Math project = $5\frac{1}{4}\ hrs$

$5\frac{1}{4}\ hrs$ can be Rewritten as $\frac{21}{4}\ hrs$

Number of Hours Carl worked on Math project = $\frac{21}{4}\ hrs$

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$6\frac{1}{2}\ hrs$ can be rewritten as $\frac{13}{2}\ hrs$

Number of Hours Sonia worked on Math project = $\frac{13}{2}\ hrs$

Number of Hours Tony worked on Math project = $5\frac{2}{3}\ hrs$

$5\frac{2}{3}\ hrs$ can be rewritten as $\frac{17}{3}\ hrs.$

Number of Hours Tony worked on Math project = $\frac{17}{3}\ hrs.$

Now Given:

April worked $1\frac{1}{2}$ times as long on her math project as did Carl.

$1\frac{1}{2}$ can be Rewritten as $\frac{3}{2}$

Number of Hours April worked on math project = $\frac{3}{2}$ $\times$ Number of Hours Carl worked on Math project

Number of Hours April worked on math project = $\frac{3}{2}\times \frac{21}{4} = \frac{63}{8}\ hrs \ \ Or \ \ 7\frac{7}{8} \ hrs$

Also Given:

Debbie worked $1\frac{1}{4}$ times as long as Sonia.

$1\frac{1}{4}$ can be Rewritten as $\frac{5}{4}$ .

Number of Hours Debbie worked on math project = $\frac{5}{4}$ $\times$ Number of Hours Sonia worked on Math project

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Richard worked $1\frac{3}{8}$ times as long as tony.

$1\frac{3}{8}$ can be Rewritten as $\frac{11}{8}$

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Hence We will match each student with number of hours she worked.

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Debbie. $8\frac{1}{8}\ hrs$

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