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:
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