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The ex- suffix often correlates a word to mean "outside", while the in- suffix often correlates a word to mean "inside". An exterior angle of a polygon would mean "an angle outside of a polygon". An interior angle of a polygon would mean "an angle inside of a polygon". Three exterior angles of this polygon would be angle B, angle D, and angle A. This is because these angles are outside of the polygon due to the extending lines from the shape. Two interior angles of this polygon would be angle 6 and angle 8 (explanation was given when I first began answering this question). Angle 9 would be exterior since it is outside of the polygon. Two exterior angles of the polygon that are congruent are angle D and angle 9, since they are both 90 degrees (right angles).
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The number of white and grey blocks in the quilts follows a sequence given by the Design number of the quilt
The numbers and patterns of the blocks are;
a. Patterns;
- The height of the white blocks is the Design number, while the rows are one more than the design number
- The height of the outer grey blocks is 2 blocks more than the Design number, while their rows are 3 blocks more than the Design number
b. The function is
c. The function is
d.
e. The design chosen is <u>Design 9</u>
The number of blocks is <u>132 blocks</u>
Reasons:
The pattern of the design are;
a. The column height of the grey blocks = 2 blocks more than the column height of the white blocks
Width of the outer grey blocks = 2 blocks more than the width of the inner white blocks
The number of white blocks in a design, <em>n</em> is the product of <em>n</em> and (n + 1)
The number of grey blocks in a design <em>n</em>, is the product of (n + 2) and (n + 3) less the number of white blocks in the design
b. Based on the above, the function that represent the number of picture blocks in Design <em>n</em>, is therefore;
- p(n) = n·(n + 1)
c. Based on the above, the function that represent the number of border blocks in Design <em>n</em>, is therefore;
- b(n) = (n + 2)·(n + 3) - n·(n + 1)
d. The total number of blocks, t(n) = (n + 2)·(n + 3)
t(n) = (n + 2)·(n + 3) - n·(n + 1) + n·(n + 1)
- t(n) = p(n) + b(n)
e. The given number of picture blocks = 90
The number of picture blocks in a design, n = n × (n + 1)
Therefore, given that the number of picture blocks is 90, we have;
90 = n × (n + 1)
n² + n - 90 = 0
(n + 10)·(n - 9) = 0
n = 9, or n = -10
Therefore, the design museum chooses is <u>Design 9</u>
The total number of blocks in a quilt design, t(n) = (n + 2)·(n + 3)
Total blocks in the design the art museum choses, t(9), is given as follows;
t(9) = (9 + 2)·(9 + 3) = <u>132 blocks</u>
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