Answer:
100
Step-by-step explanation:
sum the parts of the ratio, 4 + 5 + 1 = 10 parts
Fiona gets 40 sweets which is 4 parts of the ratio
Divide Fiona's share by 4 to find the value of one part of the ratio
40 ÷ 4 = 10 ← 1 part of the ratio
The total number of sweets is 10 parts , thus
number of sweets in total = 10 × 10 = 100
Answer:
x = 5
Step-by-step explanation:
To find the value of x make sure to get it on one side
First subtract 3x from each side. This makes the equation now
3x + 2 = -8 + 25
Now see what 25 subtract by 8 is (17)
3x + 2 = 17
Next subtract 2 from both sides
3x = 15
Lastly, divide 15 by 3, making x equal 5
x = 5
Part (A)
We have n = 5 sides, so the measure of any exterior angle of a regular pentagon is E = 360/n = 360/5 = 72
Each interior angle is therefore 180-E = 180-72 = 108 degrees.
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Alternatively, you could use the formula below with n = 5
i = interior angle
i = 180(n-2)/n
i = 180(5-2)/5
i = 180(3)/5
i = 540/5
i = 108
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<h3>Answer: 108 degrees</h3>
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Part (B)
We're told that CDF is 70 degrees. From part (A) we know that angle CDE is 108 degrees, so this must mean that angle EDF is 108-70 = 38 degrees.
Similarly, angle FEA is 85 degrees, which subtracts from angle AED to get 108 - 85 = 23 degrees. This is the measure of angle DEF.
So far we found
angle EDF = 38
angle DEF = 23
Let's call these x and y for shorthand. Let z be the missing third angle of triangle DFE.
So,
x+y+z = 180
38+23+z = 180
61+z = 180
x = 180-61
x = 119
Interior angle DFE is 119 degrees.
Note how 90 < x < 180 showing we have an obtuse angle. It is not a reflex angle because the statement 180 < x < 360 is false.
So we subtract the value of x from 360
360-x = 360-119 = 241
This is the reflex angle DFE
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<h3>Answer: 241 degrees</h3>
