Answer: x = 6
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Work Shown:
According to the remote interior angle theorem, we can add the interior angles to get the exterior angle that is not adjacent to the interior angles.
So we'll add interior angles D = 6x+8 and E = 5x+8, and that sum leads to 82.
Let's solve for x
(6x+8)+(5x+8) = 82
11x+16 = 82
11x = 82-16 ....... subtracting 16 from both sides
11x = 66
x = 66/11 ...... dividing both sides by 11
x = 6
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A slightly longer method involves letting y be the missing interior angle of triangle DEC.
Then we can say D+E+C = (6x+8)+(5x+8)+y = 180. This is because the interior angles of any triangle always add to 180.
Furthermore, we also know y+82 = 180, since the angles y and 82 are a linear pair. Solving for y leads to y = 180-82 = 98
Plug this back into the first equation and solve for x
(6x+8)+(5x+8)+y = 180
(6x+8)+(5x+8)+98 = 180
(6x+8)+(5x+8)= 180-98
(6x+8)+(5x+8) = 82 .... note how this equation shows up again
The steps to solving are shown in the previous section.
