3a)
Answer: The sum of a+b+c+d is equal to 220
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How I got this answer:
a+b+e = 180
c+d+f = 180
angles 'e' and 'f' are marked in the attached drawing below (see figure 1)
Add the two equations to get
(a+b+e)+(c+d+f) = 180+180
a+b+e+c+d+f = 180+180
a+b+e+c+d+f = 360
(a+b+c+d)+(e+f) = 360
(a+b+c+d)+(140) = 360 substutition (see below)
a+b+c+d = 360-140
a+b+c+d = 220
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3b)
The angles of the triangles add to 180 degrees each. The three angles e, f, and 40 add to 180 as well as they form a straight angle, so e+f+40 = 180 leading to e+f = 180-40 = 140. This will help us with the substitution rule I marked above
So the idea is you add up all the angles, and then take away the angles we don't want (e and f) so we end up with the sum of a+b+c+d
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4
Answer: 290
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Step-by-step explanation:
Check out the attached image figure 2.
Angle DAE is given to be 30 degrees. Angle ADC is also equal to 30 because they are alternate interior angles.
Angle DCB is 40 degrees. The missing angle x of the triangle DCB is unknown for now, but we can solve for x
x+40+30 = 180
x+70 = 180
x = 180-70
x = 110
Therefore the purple angle marked in that diagram is 180-x = 180-110 = 70
The reflex angle to the 70 degree angle is 360-70 = 290
which is the shaded angle we want to determine