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sladkih [1.3K]
2 years ago
9

If DEFG is a kite, find the measure of angle EFG

Mathematics
1 answer:
Vlad [161]2 years ago
3 0
Since kites have two distinct pairs of consecutive, congruent sides their diagonals are perpendicular and one diagonal
bisects the other.

Since perpendicular lines intersect at 90° every triangle in a kite is a right triangle. Since it is given that angle DEF is 72° and we know triangles equal 180°

72+90=162
180-162 =18

so angle EFD is 18° and because angle EFD is a bisected part of angle EFG - 18x2=36

so angle EFG is 36°
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Option 2:

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insens350 [35]
To solve using synthetic division:

Draw an upside down division symbol (I did the best I can given the format). Place the constant of x - 1 (1) on the outside, and the coefficients of x³ - 2x² - 1 on the inside, like so:      

   | x³   x²   x¹   x⁰
1 | 1   -2    0   -1   
   |         
   |___________

Next, bring down the first coefficient.

    | x³   x²   x¹   x⁰
  1| 1   -2    0   -1   
    |         
    |___________ 
      1

Multiply the number on the outside of the symbol (1) by the coefficient you've just brought down (1). Place that number under the next coefficient to the right.

    | x³   x²   x¹   x⁰
  1| 1   -2    0   -1    
    |       1   
    |___________ 
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Add the new number (1) to the coefficient above it (-2) and place that number directly underneath it.

    | x³   x²   x¹   x⁰
  1| 1   -2    0   -1    
    |       1   
    |___________ 
      1   -1

Continue this process until you've run out of numbers to multiply.

    | x³   x²   x¹   x⁰
  1| 1   -2    0   -1    
    |       1   -1   -1
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      1   -1   -1   -2

The resulting numbers are coefficients. The first three are part of the quotient, and the last one is part of the remainder. The remainder becomes the last coefficient (-2) over the divisor (x - 1).

Answer:
(x³ - 2x² - 1) / (x - 1) = x² - x - 1 + -2/x - 1
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