In the parallelogram below find the value of each variable. Hint: find the value of t first
Answers
Answer:
because this is a parallelogram
=> 3t - 15 = 2t + 10
⇔ t = 10 + 15
⇔ t = 25
with t = 25 => 3t - 15 = 3.25 - 15 = 60
we also have:
4r + (3t - 15) = 180°
⇔ 4r + 60° = 180°
⇒ 4r = 120°
⇔ r = 30
we also have;
4r = 3s
=> 4.30 = 3s
⇔ s = 4.10
⇔ s = 40
Step-by-step explanation:
You can use the fact that sum of all angles of a parallelogram is 360 degrees and the sum of two adjacent angles in a parallelogram is 180 degrees.
The value of the variables used in the figure are:
r = 30
s = 40
t = 25
What are some useful properties of angles of a parallelogram?Sum of all angles of a parallelogram is 360 degrees.Sum of two adjacent angles in a parallelogram is 180 degrees.Using the above facts to find the values of specified variables[tex]4r + (3t - 15) + (2t + 10) + 3s = 360^\circ\\4r + 3s + 5t = 365[/tex]
And
[tex]3t - 15 + 4r = 180 \cdots (1)\\3t - 15 + 3s = 180\cdots (2)\\3s + 2t + 10 = 180\cdots (3)\\4r + 2t + 10 = 180\cdots (4)[/tex]
We get 2 systems of linear equations.
First system consists of equation 1 and equation 4
Second system consists of equation 2 and equation 3
From equation 1 and 4, as both's left side is equal to 180, thus they are equal too, or
[tex]3t - 15 + 4r = 4r + 2t + 10\\3t - 2t = 4r - 4r + 10 + 15\\t = 25[/tex]
Putting it in equation 1, we get:
[tex]3t - 15 + 4r = 180\\3 \times 25 + 4r = 180 + 15\\75 + 4r = 195\\\\r = \dfrac{195 - 75}{4} = 30[/tex]
Putting the value t = 25 in second equation, we get:
[tex]3t - 15 + 3s + 180\\3 \times 25 - 15 + 3s = 180\\60 + 3s = 180\\\\s = \dfrac{180 - 60}{3} = 40[/tex]
Thus, the values of the specified variables in the given graph are:
r = 30
s = 40
t = 25
Learn more about system of linear equations here:
: https://brainly.com/question/13722693
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Answers
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Problem 4
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Refer to the diagram below. Note how I've added in the variable y and marked another angle as 53 degrees which is one of the base angles of the left triangle. The base angles of the triangle on the right are y degrees each. Also, note the vertical angles both are y.
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==================================================
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Answers
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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Answers
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========================================================
Explanation:
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