The measure of ∠BAF is 54°.
Solution:
DF and CE are intersecting lines.
m∠EAF = 72° and AB bisects ∠CAF.
∠EAF and ∠DAC are vertically opposite angles.
Vertical angle theorem:
<em>If two lines are intersecting, then vertically opposite angles are congruent.</em>
∠DAC ≅ ∠EAF
m∠DAC = 72°
<em>Sum of the adjacent angles in a straight line = 180°</em>
m∠DAE + m∠EAF = 180°
m∠DAE + 72° = 180°
Subtract 72° from both sides.
m∠DAE = 108°
∠CAF and ∠DAE are vertically opposite angles.
⇒ m∠CAF = m∠DAE
⇒ m∠CAF = 108°
AB bisects ∠CAF means ∠CAB = ∠BAF
m∠CAB + m∠BAF = 108°
m∠BAF + m∠BAF = 108°
2 m∠BAF = 108°
Divide by 2 on both sides, we get
m∠BAF = 54°
Hence the measure of ∠BAF is 54°.
Answer:
Tom's share = €800
Step-by-step explanation:
Given that:
Amount shared by Al, Tom and Joe = €3000
Ratio of Al's share to Tom's share = 5 : 4
Joe's share = 1.5(Tom's share) = 1.5(4) = 6
Therefore,
Ratio of Al, Tom and Joe = 5 : 4 : 6
Let,
x be the number of times of amount each get.
5x + 4x + 6x = 3000
15x = 3000
Dividing both sides by 15
Tom's share = 4x = 4(200) = €800
Hence,
Tom's share = €800
Answer:
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Step-by-step explanation:
The answer by the sequence:
Width of the garden = w
Length of the garden = 2w+3
Width of the entire plot = w + 0.5w = 1.5w
Length of the entire plot = (2w + 3) 0.5w = 2.5w + 3
Area of the garden = w (2w + 3)
Area of the entire plot = 1.5w (2.5w + 3)
Area of the garden = 2w² + 3w
Area of the entire plot = 3.75w² + 4.5w
Area of border = area of the entire plot - area of the garden
= 3.75w² + 4.5w - (2w² + 3w)
Area of the border = 3.75w² + 4.5w - 2w² - 3w
Area of the border = 1.75w² + 1.5w
Answer:
no solution is ur right answer
Step-by-step explanation:
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