How do you solve this problem in the photo?
2 answers:
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Given: The shape is a quadrilateral, which means four angles with a sum of 360°. The known measures are 112 and 73, and there are two unknown measures. They are probably identical, considering the fact that they both have the variable x.
Numerically, this would be .
Simplify.
= 360
-->
Isolate the variable by subtracting 185 from both sides.
--> 2x = 175
If 175 is twice as much as x, then
x =
Plug in the value of x:
-->
X has an angle measure of 87.5°
Since <em>N</em>/2 leaves a remainder, <em>N</em> must be odd and ends with 1, 3, 5, 7, or 9.
<em>N</em>/5 also leaves a remainder, so <em>N</em> is not divisible by 5, so it does not end in 5.
The only correct choice is then 9, since
1 = 0•5 + 1 and 1 = 0•2 + 1
3 = 0•5 + 3 and 3 = 1•2 + 1
7 = 1•5 + 2 and 7 = 3•2 + 1
9 = 1•5 + <u>4</u> and 9 = 4•2 + <u>1</u>
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Alternatively, the given information is equivalent to saying
Then you can use the Chinese remainder theorem to find <em>N</em>.