URGENT MATH HELP! ANSWER

Question

Find the value of x. Then find the measure of each labeled angle.

X DEGREES = ____ DEGREES

Answer 1

In the diagram, the red “stair-step” in the lower left corner means that this is a “right angle”, which is 90°.

The red arrows mean that the two horizontal lines (the upper side and the lower side of the figure) are horizontal (and parallel). That makes the unmarked angle at the upper left a right angle also (90°).

Now, use your imagination: In the 1960’s, Seymour Papert and his team at MIT developed a computer-controlled “turtle” with a pen that you place on a sheet of paper to draw figures. If the turtle started at the lower left corner facing right, traveled, turned left (x-46) degrees, traveled, turned left x degrees, traveled, turned left 90 degrees, traveled, then turned left 90 degrees, then STOPPED, it would have turned around completely – that is a full 360° (like a full circle) !

So, 90 + 90 + x + (x-46) = 360

Or, since the top and the bottom lines are parallel, x + (x-46) = 180

    2x – 46 = 180

     2x = 226     [add 46 to both sides]

       x = 113 degrees [divide both sides by 2]

Also, (x-46) = 67

Answer 2

The sum of the angles = 360 degrees, the two angles on the left side are 90 each total of 180 degrees then:

x + x - 46 = 180

2x = 226

x = 113 degrees

then x = 113 degrees

x - 46 = 67 degrees