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Rus_ich [418]
3 years ago
7

Find the measure of b

Mathematics
2 answers:
Yanka [14]3 years ago
5 0
<h3>Answer:  100</h3>

========================================================

Explanation:

Let's add angle c to the diagram such that it's adjacent to angle b, and inside the quadrilateral. Notice how angle c is opposite the 100 degree angle of this inscribed quadrilateral.

For any inscribed quadrilateral, the opposite angles are supplementary

c+100 = 180

c = 180-100

c = 80

Angles b and c are supplementary as well, because they form a straight line.

b+c = 180

b+80 = 180

b = 180-80

b = 100

In short, angle b is the same measure as that 100 degree angle in the diagram.

VMariaS [17]3 years ago
5 0

Step-by-step explanation:

Hi there!

From the above figure;

Let "x" be an unknown angle.

Then;

100° + X = 180°. { The opposite angles of cyclic quadrilateral is supplementary}

X = 180°-100°

Therefore, X= 80°.

Now;

X+b = 180°. {linear pair}

80° + b = 180°

Therefore, b = 100°.

[Next method:

b = 100° {When any side of cyclicquadrilateral is extended the external angle is equal to opposite interior angle.]

<u>Hope</u><u> it</u><u> helps</u><u>.</u>

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What are the side lengths of the rectangle area 40 perimeter 26
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Recall the formula for finding the area of a rectangle:

           Area = Length × Width

Recall the formula for finding the perimeter of a rectangle:

         Perimeter = 2 ( Length + Width )

Given in your problem:
        Area = 40 sq. units
        Perimeter = 26 units

Required to solve for:
        Length (L) and width (W)

• First, substitute the given to the formula:

        Area = Length x Width
          40 = L × W      ⇒   equation number 1

       Perimeter = 2 ( Length + Width )
            26 = 2 ( L + W )     ⇒   equation number 2


• Simplifying equation number 2,
           13 = L + W

 • Rearranging the equation, 

         L = 13 - W   ⇒   equation 3

Substituting equation 3 from equation 1:

      ( equation 1 )               40 = (L)(W)
      ( equation 3 )                L = 13 - W
                                      40 = (13 - W) (W)
                                      40 = 13W - W² 
      ( regrouping )          W² - 13W + 40 = 0
      ( factoring )             (W - 8) (W - 5) = 0
                                     W - 8 = 0    ;     W - 5 = 0
                                        W = 8      ;        W = 5
   
Therefore, there are 2 possible values for the width of the rectangle. It can be 8 units or 5 units.

• Now to solve for the length of the rectangle, substitute the two values of width to equation 3.

      (equation 3)        L = 13 - W
                       for W = 8    ⇒   L = 13 - 8
                                                   L = 5 units
                   
                       for W = 5    ⇒  L = 13 - 5
                                                   L = 8 units

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2 years ago
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