If line ad is parallel to line eh, and the measure of angle i is 52 degrees and the measure of angle fbc is 42 degrees, what is the measure of angle igf?

∠IGF = 86°

Step-by-step explanation:

Given AD and EH are parallel, then

∠GFI = ∠FBC = 42° (corresponding angles )

The sum of the 3 angles in a triangle = 180°

Subtract the 2 angles in ΔFGI from 180 for ∠IGF

∠IGF = 180° - (52 + 42)° = 180° - 94° = 86°

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

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