Question

Raghav, Rajit, Junsu, Mia, and Umema were finished with lunch and began playing with drink straws. Each one was making a line design using either 3 or 4 straws. Since they had just come from math class where they had been studying special angles, Raghav pulled his pencil out of his bookbag and labeled some of the angles and lines. He then challenged himself and the others to find the values of x and y in degrees.

Show how you would find the values of x and y for Raghav’s straw figure shown below using a system of linear equations. (You may use a decimal to the tenths place for your answers for the angle measures.)

Answer 1

x =
`25.8^(o)` and y =
`51.4^(o)`

Explanation:

Known that he sum of angles on a straight line is
`180^(o)`. From the diagram;

2y + x + y =
`180^(o)`

x + 3y =
`180^(o)` ................ 1

Also,

2x + x + 2y =
`180^(o)`

3x + 2y =
`180^(o)` .............. 2

Using the elimination method, multiply equation 1 by 3 and equation 2 by 1

3x + 9y = 540 ............ 3

3x + 2y =
`180^(o)` ............. 4

7y = 360

y =
`(360)/(7)`

y =
`51.4^(o)`

substitute the value of y in equation 1,

x + 3y =
`180^(o)`

x + 3(51.4) =
`180^(o)`

x + 154.2 =
`180^(o)`

x =
`180^(o)` - 154.2

x =
`25.8^(o)`

Thus, x =
`25.8^(o)` and y =
`51.4^(o)`