Answers:
- a = 69
- b = 47
- c = 116
- d = 93
- e = 86
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Step-by-step explanation:
For now, focus on the triangle with angles 'a', 71 and 40 degrees.
Recall that for any triangle, the inside angles always add to 180
a+71+40 = 180
a+111 = 180
a = 180-111
a = 69
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Notice how angles b and 133 are adjacent and form a straight angle. This makes them supplementary. Meaning they add to 180
b+133 = 180
b = 180-133
b = 47
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Let angle f be adjacent to angle c, and part of the triangle with angles 'a' and b.
Use the rule mentioned in the first section
a+b+f = 180
69+47+f = 180
116+f = 180
f = 180-116
f = 64
Now we can find angle c, because angles f and c are supplementary
c+f = 180
c+64 = 180
c = 180-64
c = 116
We could also use the remote interior angle theorem to say that a+b = c, so c = a+b = 69+47 = 116
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Next, focus your attention on the 140 degree angle. The missing adjacent angle to this is 180-140 = 40 degrees
Now focus on the triangle that has angles d, 40, and 47. The "40" being what we just calculated in the previous paragraph.
We'll do the same thing as before
d+40+47 = 180
d+87 = 180
d = 180-87
d = 93
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The angle just above angle d is also the same (vertical angles). This upper triangle has angles 40, d and g, where g is unknown. Let's find it.
40+d+g = 180
40+93+g = 180
133+g = 180
g = 180-133
g = 47
The vertical angle across from this is also 47 degrees.
Similarly, we can move that angle b over to its vertical pairing counterpart.
The smallest triangle at the very top has angles e, b, and g
e+b+g = 180
e+47+47 = 180
e+94 = 180
e = 180-94
e = 86