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
Found 2 solutions by Theo, ikleyn:
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.
Answer by ikleyn(52832)  (Show Source):
You can put this solution on YOUR website! .
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?
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Calculations in the post by tutor @Theo are incorrect.
I came to bring a correct solution.
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 degrees
combine like terms to get:
7x-1 = 90
add 1 to both sides of the equation to get:
7x = 91
divide both sides of the equation by 7 to get:
x = 91/7 = 13.
angle FGH is equal to 4x which makes it equal to 4*13 = 52 degrees.
angle ABE is equal to 3x-1 which makes it equal to 3*13-1 = 38 degrees.
add them together to get 90 degrees
the numbers check out.
angle ABE is equal to 38 degrees
angle CBD is equal to angle ABE and so is equal to the same.
ANSWER. Angle CBD is 38 degrees..
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Solved correctly.
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