9514 1404 393
Answer:
- x = 23
- x = 25
Step-by-step explanation:
1. Each of the angles shown is an external angle to the adjacent internal angle of the quadrilateral. The sum of the angles of the quadrilateral is 360°. The internal angle is the supplement of the external angle.
(180 -(x +16)) +(180 -(3x -1)) +(180 -6x) +(180 -5x) = 360
705 -15x = 360 . . . . . collect terms
47 -x = 24 . . . . . . . . . . divide by 15
47 -24 = x = 23
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2. The sum of the angles of a pentagon is 540°, so we have ...
(5x +5) +2(4x -10) +2(4x +15) = 540
21x +15 = 540 . . . . simplify
21x = 525 . . . . . . . .subtract 15
x = 25 . . . . . . . . . . . divide by 21
