Answer:
1) 128°
2) 126°
3) 108°
Question one:
The square in the corner means 90°. If you add the interior angles of any triangle together, you get 180. in this case, x is in exterior angle, so you subtract it from 180 to get the interior angle.
38 + 90 + (180-x) = 180
38 + 90 + 180 - x = 180
38 + 90 + 180 - 180 - x = 0
38 + 90 + 180 - 180 = x
128 = x
Question two:
again, adding all the interior angles makes 180°. use this to make the equation.
3x + (5x-6) + 90 = 180
3x + 5x - 6 = 90
8x = 96
x = 12.
x isn't the answer the question wants, however. if you look at the drawing, the angle that's supplementary to 5x-6 is the exterior angle. so,
180 - (5x-6) = the answer
180 - 5x + 6 = the answer
substitute x for 12
180 - 60 + 6 = the answer
126 = x
Question three
again, adding all the interior angles together makes 180°.
(a + 10) + 44 + (180-2a) = 180
a + 10 + 44 + 180 - 2a = 180
-a + 234 = 180
234 - 180 = a
54 = a
however, the question is looking for the exterior angle, not a. in this case, the exterior angle is 2a, so just multiply 54 by 2.
x = 108