Answers:
- x = 8
- angle HIJ = 175 degrees
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Work Shown:
(angle HID) + (angle DIJ) = angle HIJ
(100) + (8x+11) = 21x+7
100+8x+11 = 21x+7
8x+111 = 21x+7
111-7 = 21x-8x
104 = 13x
13x = 104
x = 104/13
x = 8
Use this x value to find angle HIJ
angle HIJ = 21x+7
angle HIJ = 21*8+7
angle HIJ = 175 degrees
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Extra info:
You can also use that x value to find angle DIJ
angle DIJ = 8x+11
angle DIJ = 8*8+11
angle DIJ = 75
Then add this to angle HID to get
angle HID + angle DIJ = 100+75 = 175
This matches with angle HIJ = 175
So this confirms angle HID + angle DIJ = angle HIJ which helps confirm our answers.