<p>Okay so the first two I got it right, but I was just wondering if there is a mathematical way to solve it.</p>
<p>Here is an algebraic solution to the first one:</p>
<p>Let x be the sum of the two smaller angles. Then the larger angle is 2x, and x+2x=180. So 3x=180, and x=60. The largest angle is 2x=120.</p>
<p>Note that this is NOT the way I would do it on the SAT.</p>
<p>For the third one we have</p>
<p>1-1/2+1/2-1/3+1/3-…+1/50-1/51 = 1-1/51 = 50/51.</p>
<h1>1)Smallest = x</h1>
<p>Largest = 2(x + x)</p>
<p>2(x + x) + 2x = 180
2(2x) + 2x = 180
4x + 2x = 180
6x = 180
x = 30
Smallest Angle = 30
Largest = 120</p>
<p>For the second one, the diagonals of a square split the square into four 45 45 90 right triangles (isosceles right triangles). From the picture we see that a leg of 1 of these triangles has length 1.5. So you must either add or subtract 1.5 to 2 to get the y-coordinate of the point. Thus the point is (1.5, 3.5).</p>
<h1>2)You have to imagine a diagonal</h1>
<p>and come up with a formula…</p>
<p>Mid point:
(x1 + x2)/2, (y1 + y2)/2
(0 + 3)/2, (2 + 2)/2
Mid point of the diagonal: (1.5, 2)
If this diagonal was a side ways one, it would require a vertice at this x location (1.5).</p>
<p>A square’s sides are equal, so it’s diagonals are equal as well. This means you should move up 1/2 of the diagonal.</p>
<p>The length of the diagonal is 3 units.
(1.5,(2 + 3/2))
Answer: (1.5,3.5)</p>
<p>DRSTEVE: Your explanation for the third one blew my mind. Wow, after reading what you wrote I’m just “WOW THAT’S SO SIMPLISTIC!?!?” Thank you so much for all explanations. And my I ask how would you solve number 1?</p>
<p>COLUMBIANX: Thank you especially number 1 & 2. I now understand :].</p>
<p>For the third problem, you can just make a short list of the sums of the first values they give you.
1/2
(1/2 + 1/6)
(1/2 + 1/6 + 1/12)</p>
<p>=
1)1/2
2)2/3
3)3/4
4)4/5
50)?
And you can convert that into a quadratic equation.
Though, you might be easily able to see the pattern from the values.
And come up with 50/51.</p>
<p>For the first one I would start with choice C. If the larger angle is 90, the sum of the other 2 is 90. So the larger is NOT double the sum. This we can eliminate choices A, B and C. Let’s try D next. If the largest angle is 120, the sum of the other 2 is 60, and this works.</p>
<p>drsteve: lol that’s what i did (:</p>
<p>Lol I feel as if I’m making these problems more difficult than is needed.</p>
<p>Haha it’s okay. That’s what CC do (well sometimes d: ) (:</p>
<p>Great! That’s the way to do it on the SAT. But keep in mind that when practicing you should try to solve each problem as many ways as possible. The more ways you solve each problem, the deeper understanding you will have of the underlying mathematics - and this translates to being able to solve more problems in the future.</p>