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Answers:

  • EG = 26 units
  • angle IFG = 40 degrees

Input the numbers only.

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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

  • i = 100
  • F = x
  • G = x

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.

Answer:

EG = 26 units

angle IFG = 40 degrees

Step-by-step explanation:

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