Answer:
(a, b, c) = (30°, 60°, 105°)
Step-by-step explanation:
Angle "a" and 30° are vertical angles, hence equal.
Angle "b" and angle "a" are complementary angles, so b = 90° -30° = 60°.
Angle "c" is supplementary to the one marked 75°, so is 180° -75° = 105°.
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Angles "a" and "b" are complementary because the sum of angles in a triangle is 180° and the third angle in that triangle is 90°. Then ...
a+b = 180°-90° = 90°
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75° and "c" are supplementary, because they are linear angles. The angle measure of a line is 180°, so that is their total measure.
Answer:
Three (3) is the correct answer
Answer:
FG = 18
Step-by-step explanation:
FD is an angle bisector and divides the opposite side into segments that are proportional to the other 2 sides, that is
= 
( cross- multiply )
54x = 24(x + 10)
54x = 24x + 240 ( subtract 24x from both sides )
30x = 240 ( divide both sides by 30 )
x = 8
Then
FG = x + 10 = 8 + 10 = 18
Remove parentheses
3m - 7m+12 = 2 m-3
collect like terms
3m-7m-12 = 2m-6
move terms
-4m - 12 = 2m-6
collect the like terms and calculate
-4m-2m = -6+12
divide both sides by -6
-6m=6
m= -1
