Answer:
The answer is 8.25 ( No CALCULATORS) - solves from my brain :)
Step-by-step explanation:
99 divided by 12 in decimal = 8.25
99 divided by 12 in fraction = 99/12
99 divided by 12 in percentage = 825%
a)
Each angle of the equilateral triangle is 180/3 = 60 degrees. Each angle of the square is 90 degrees. Focus on the angles around the top vertex of the equilateral triangle. We have 2 angles from the square and one angle from the equilateral triangle, so 2*90+60 = 180+60 = 240 degrees is accounted for so far, leaving 360-240 = 120 degrees left over for the northernmost triangle.
The northernmost triangle is isosceles because the squares all have the same side lengths (due to the fact they match up with an equilateral triangle where all the sides are the same here as well). Isosceles triangles have congruent base angles, in this case both are x degrees. Add up the angles of this northernmost triangle and set this equal to 180. Solve for x.
x+120+x = 180
2x+120 = 180
2x = 180-120
2x = 60
x = 60/2
x = 30
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b)
The angle x combines with the 90 degree adjacent angle of the square to get 90+x = 90+30 = 120. Each interior angle of this odd hexagon is 120 degrees. Focus on the entire figure overall.
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c)
The interior angles of any pentagon always add to 180(n-2) = 180(5-2) = 540 degrees. Assuming this is a regular pentagon, each interior angle of the regular pentagon is 540/5 = 108 degrees.
Focus on the northern most point on the pentagon. The angles attached to this point are the two square angles of 90 degrees each and the 108 degrees from the interior angle of a pentagon. We have 2*90+108 = 288 degrees so far, and 360-288 = 72 degrees left over for the bottom angle of the northern most triangle.
Again we have an isosceles triangle, so the base angles are both x
x+x+72 = 180
2x+72 = 180
2x = 180-72
2x = 108
x = 108/2
x = 54
And,
90+x = 90+54 = 144 represents each interior angle of this strange looking decagon.
Answer:
9 cm
Step-by-step explanation:
L = 5+3W
P = 82
=> P = 2L + 2W
82 = 2(5+3W) +2W
82 = 10+6W+2W
82 = 10+8W
8W = 82-10
8W = 72
W = 72/8
W = 9
so, the width = 9 cm
Answer:
Step-by-step explanation:
From the figure,
<h3>∠1 = ∠2 </h3>
- (Alternate angles are equal)
<u>We know that:</u>
- ∠1 = 10x + 2
- ∠2 = 12x - 22
So,
<h3>10x + 2 = 12x - 22</h3>
Add 22 to both sides
10x + 2 + 22 = 12x
10x + 24 = 12x
Subtract 10x to both sides
24 = 12x - 10x
24 = 2x
Divide 2 to both sides
12 = x
OR
<h3>x = 12</h3>
Given that,
∠2 = 12x - 22
Put x = 12
∠2 = 12(12) - 22
∠2 = 144 - 22
<h3>∠2 = 122°</h3>
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Answer:
Step-by-step explanation:
<u>Connect the center with A and C:</u>
<u>Use Pythagorean to find half of AB:</u>
<u>Similarly, find the length of CD:</u>
