Answer:
Step-by-step explanation:
we know that
The area of the trapezoid is equal to
step 1
Find the measure of angle DAE
m∠ADC+m∠DAE=180° -----> by consecutive interior angles
we have
m∠ADC = 134°
substitute
134°+m∠DAE=180°
m∠DAE=180°-134°=46°
step 2
In the right triangle ADE
Find the length side AE
cos(∠DAE)=AE/AD
step 3
In the right triangle ADE
Find the length side DE
sin(∠DAE)=DE/AD
step 4
Find the area of ABCD
we have
substitute
Length (2, 6) to (-4, 6) is sqrt((x2 - x1))^2 + (y2 - y1)^2) = sqrt((-4 -2)^2 + (6 - 6)^2) = sqrt((-6)^2 + 0) = 6
Length (2, 6) to (-4, 4) is sqrt((-4 - 2)^2 + (4 - 6)^2) = sqrt((-6)^2 + (-2)^2) = sqrt(36 + 4) = sqrt(40) = 2sqrt(10) units
Length (-4, 6) to (-4, 4) is sqrt((-4 - (-4))^2 + (4 - 6)^2) = sqrt(0^2 + (-2)^2) = 2
Therefore, the length of the longest side is 2sqrt(10) units
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Find x :
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Sum of adjacent angles on a straight line is 180.
∠ABY + ∠YBC = 180
x + 25 + 2x + 50 = 180
3x + 75 = 180
3x = 105
x = 35
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Check if AC is parallel to DF :
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If AC is parallel to DF,
∠YBC = ∠BEF (Corresponding angles)
∠YBC = 2x + 50 = 2(35) + 50 = 120
∠BEF = 5x - 55 = 5(35) - 55 = 120
Since ∠YBC = ∠BEF, AC and DF are parallel.
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Answer: Since ∠YBC = ∠BEF, AC and DF are parallel.
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Answer:
y = 394
Step-by-step explanation:
