18c) Find the value of x in each case.
1 answer:
Answer:
x = 22.5°
Step-by-step explanation:
m∠DEA = 2x
DE || AB
m∠EAB = 2x - by Alternate Interior Angles
Exterior angle = 6x, which equals 2x + 4x
m∠BEA = 4x
Exterior Angle 4x = 2x + 2x
m∠B = 2x
2x + 4x + 2x = 180°
8x = 180°
x = 22.5°
<h2>Exterior Angles of a Triangle:</h2>An exterior angle of a triangle is equal to the two REMOTE angles inside the triangle.
In this example, we know that 6x has remote angles of ∠EAB and ∠BEA
We found out that m∠EAB = 2x, so m∠BEA must equal 6x - 2x or 4x
<h2>Sum of angles in a Triangle:</h2>The sum of all angles in a triangle is equal to 180°.
In this example, we found all the angles, 2x, 4x, 2x. We added all of those values to equal 8x
Since the sum of all angles = 180°:
8x = 180°
x = 180°/8
x = 22.5°
-Chetan K
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Answer:
The Area of Rectangular Garden is 1044 feet²
Step-by-step explanation:
According to question
The perimeter of the garden = 82 ft
Let the length be L ft
The width be W ft
Now as per question
L = 5 + ( 2× W )
∵ Perimeter of Rectangle = 2 × ( Length + Width )
Or , Perimeter of Rectangle = 2 × ( L+ W )
Or, 82 = 2 × ( L+ W )
Or, 82 = 2 × [ 5 + ( 2 ×W ) + W ) ]
Or, 82 = 2 × ( 5 +3W )
Or, 41 = 5 + 3W
Or, 41 - 5 = 3W
So, 3W= 36
∴ W = = 12 feet
I.e Width = 12 feet
And L = 5 + ( 2× W )
Or, Length = 5 + 24 = 29 feet
Now The Area of Rectangle = Length × width
So, The Area of Rectangle = 29 ft × 36 ft
The Area of Rectangle is 1044 feet²
Hence The Area of Rectangular Garden is 1044 feet² Answer
Answer:
Option A is the correct choice.
Step-by-step explanation:
Let d be the number of boxes of duck calls and t be the number of boxes of turkey calls.
We have been given that a company sells boxes of duck calls for $35 and boxes of turkey calls (t) for $45, so the revenue earned from selling d boxes of duck and t boxes of turkey call will be 35d and 45t respectively.
Further, the company plan to make $300. We can represent this information as:
We are also told that they make batches of duck calls that fill 6 boxes and batches of turkey calls that fill 8 boxes. the company only has 42 boxes. We can represent this information as:
Therefore, our desired system of equation will be: