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Step-by-step explanation:

1. The sum of all angles in a triangle is 180°

75° + 60° + x° = 180°

135° + x° = 180°

x° = 55°

2. The sum of all angles in a triangle is 180°

70° + 70° + x° = 180°

140° + x° = 180°

x = 40°

3. The sum of all angles in a triangle is 180°

1 : 2: 5 = 1x:2x:5x

1x + 2x + 5x = 180°

8x = 180°

x = 22.5°

2x = 45°

5x = 112.5°

4. The sum of all angles in a triangle is 180°. The angle in a line is 180°

Missing angle is 180° - 123° = 57°

The sum of angles in a triangle is 180°

57* + x° + 90* = 180°

57° + x° = 90°

x = 33°

5. We know that the sum of angles in a triangle is 180°. We can subtract the values of the two other angles from 180* to find the missing angle.

-Chetan K

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