Answers:
- EG = 26 units
- angle IFG = 40 degrees
Input the numbers only.
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Step-by-step explanation:
In any rectangle the diagonals are the same length. Also, the diagonals cut each other in half (aka bisect).
This means EI and FI are the same length
EI = FI
4x+5 = 6x+1
4x-6x = 1-5
-2x = -4
x = -4/(-2)
x = 2
This then leads to
- EI = 4x+5 = 4(2)+5 = 13
- FI = 6x+1 = 6(2)+1 = 13
Both are 13 units long to help confirm we have the correct x value.
If EI = 13, then EG = 2*EI = 2*13 = 26 since EG is twice as long as EI. This goes back to the fact that the diagonals cut each other in half.
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If angle EIH is 100 degrees, then so is angle FIG (they are vertical angles).
Focus on triangle FIG. We just found that angle i = 100. This triangle is isosceles with FI = IG being the two equal sides. The angles opposite these congruent sides are angles F and G. Let's call them x for now.
So we have
The three angles of this triangle add to 180
F+I+G = 180
x+100+x = 180
2x+100 = 180
2x = 180-100
2x = 80
x = 80/2
x = 40
So angle F, of triangle FIG, is 40 degrees
This is the same as saying angle IFG is 40 degrees.