Answers:
x = 72
y = 83
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Explanation:
Angle VFG is 50 degrees. The angle adjacent to this is angle EFG which is 180-50 = 130 degrees.
Angle HDW is 77 degrees. The supplementary angle adjacent to this is 180-77 = 103 degrees which is angle EDH.
Pentagon EFGHD has the following five interior angles
- E = x
- F = 130
- G = 170
- H = 65
- D = 103
Note that angles F = 130 and D = 103 were angles EFG and EDH we calculated earlier.
For any pentagon, the interior angles always add to 180(n-2) = 180(5-2) = 180*3 = 540 degrees.
This means,
E+F+G+H+D = 540
x+130+170+65+103 = 540
x+468 = 540
x = 72
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Now focus your attention on triangle THS
We see that the interior angles are
The angle H is 65 degrees because it's paired with the other 65 degree angle shown. They are vertical angles.
For any triangle, the angles always add to 180
T+H+S = 180
y+65+32 = 180
y+97 = 180
y = 180-97
y = 83
Answer:
2/5
Step-by-step explanation:
To get the ratio as a pure number, it must be expressed as the quotient of two values that have the same units. For the purpose here, it is convenient to convert both values to units of seconds.
__
<h3>units conversion</h3>
The conversion factor between minutes and seconds is ...
1 minute = 60 seconds
Multiplying this equation by 3 gives ...
3 minutes = 180 seconds
__
<h3>ratio of interest</h3>
Then the desired ratio is ...
(72 seconds)/(3 minutes) = (72 seconds)/(180 seconds) = 72/180
= (36×2)/(36×5)
= 2/5
The ratio in its simplest form is 2/5.
Answer:
b
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
70^2 = 4900 < 5607 < 6400 = 80^2
so sqrt(5607) is a two-digit number with tenth-digit 7
71^2 = 5041, 72^2 = 5184, 73^2 = 5329, 74^2 = 5476, 75^2 = 5625
so the smallest square bigger than 5607 is 75^2, which is 5625
so the number should ne 5625 - 5607 = 18
