Question 556812: ANGLE ABE AND ANGLE CBD ARE VERTICAL ANGLES AND BOTH ARE COMPLEMENTARY WITH ANGLE FGH, IF m ANGLE ABE = (3x-1) AND m ANGLE FGH = (4x), what is m ANGLE CBD?
THIS IS THE CORRECT QUESTION..MESSED UP THE ONE BEFORE THIS
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if angle ABE and CBD are vertical angles, then their measure are equal.
if angle ABE is equal to (3x-1) and angle FGH = (4x), then angle CBD must also be equal to (3x-1).
to find the value of x, we use the equation of angle ABE + angle FGH = 90 degrees because they are complementary.
since ABE = 3x-1 and FGH = 4x, this means that:
3x-1 + 4x = 90
combine like terms to get:
7x-1 = 90
add 1 to both sides of the equation to get:
7x = 89
divide both sides of the equation by 7 to get:
x = 89/7
angle FGH is equal to 4x which makes it equal to 356/7
angle ABE is equal to 3x-1 which makes it equal to 274/7
add them together to get 630/7
divide that by 7 to get 90.
the number check out.
angle ABE is equal to 274/7 degrees which is equal to 39.14285714 degrees.
angle CBD is equal to angle ABE and so is equal to the same.
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