Please help will give brainliest and 80 points
2 answers:
Answer:
Start
A2
B2
B1
C1
C2
D2
D3
D4
C4
END
Step-by-step explanation:
Start (A3)
x is equal to 141 because they are alternate interior angles.
A2. x is equal to 39 because they are corresponding angles.
B2. x would be supplementary to 41 because the angle that x supplements is corresponding to 41.
41 + x = 180 due to the linear pair postulate. Therefore, x = 139.
B1. x would be supplementary to 82 because they are consecutive exterior angles.
82 + x = 180 due to the linear pair postulate. Therefore, x = 98.
C1. x = 102 due to the vertical angles theorem.
C2. x would be supplementary to 130 because the angle that x supplements is equal to 130 (Alternate Exterior Angles).
130 + x = 180, x = 50.
D2. x = 74, corresponding angles.
D3. x = 83, corresponding angles.
D4. x = 95, corresponding
C4. x is supplementary to 18 because of the consecutive interior angles theorem.
x = 162
END
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Let's carry this math sentence over to its natural, "shapey" element. We're going to look at each term not as an ordinary number, but as <em>the area of some shape</em>.
x² (read as "x <em>squared"</em>) can be seen as the area of a square with side lengths of x. 2x can similarly be seen as the area of a <em>rectangle </em>with a length of x and a width of 2. (Picture 1)
What's our question actually asking, though? Something about <em>perfect squares</em>. More specifically, we're looking for something to add on that'll <em>make this thing a perfect square</em>. We're trying to find a missing piece we can slot in to make a square, in other words. Problem is, our shapes don't look much like a square if we put them together right now. We need to do a little cutting and gluing first.
First, we're gonna cut the 2x rectangle lengthwise, getting two rectangles with an area of x, a length of 1, and a width of x. Next, we're going to attach them to the x² square, creating this shape that looks, strangely, like a square with a little bit missing from it (picture 2). What we're trying to do is <em>complete this square, </em>to find the area of that little missing chunk.
As it turns out, we have all the information we need for this. Notice that, using the lengths of the x rectangles, we can find that the square's dimensions are 1 x 1, which means that its area is 1 x 1 = 1.
If we tack this new area on to our original expression, we've "completed the square!" We now have a perfect square with side lengths of (x + 1) and an area of (x + 1)² (picture 3).
So, our final expression is x² + 2x + 1, and the missing constant - the area of the "missing square" we had to find to complete our larger one - is 1.
