<p>Hello all,</p>
<p>I was wondering if you could help me out with these two challenging math questions?</p>
<p>They are diagrams with the questions written next to them...</p>
<p>Thanks!</p>
<p>First one is 8 (b).
Second one is 180 - a - b (c).</p>
<p>Explanations:
1.
Let x be the distance from Q to line BA. Let y be the distance from Q to line CD. x + y = 4. The distance from P to BA is the same as the distance from Q to BA, same for R. So P to BA = x, R to CD = y. So the inside lines are 4, the outside lines are 4. Total is 8.</p>
<p>2.
You know that the angles in a triangle add to 180. Now you can fill in all the info. If a triangle has angles a and b, the remaining must be c, etc. because all the triangles have 180 degrees. Now, on the left leg of the triangle, the point where the inner triangle meets the leg should have three angles. Now, assuming you have a diagram with all the angles filled in, it should look like a, c, c from the top down. It's a line, so a + c + c = 180. Now, the triangles have a, b, and c, and they add to 180. So a + b + c = 180 = a + c + c. So b = c. a + c + c = 180. 180 - a - c = c. b = c, so 180 - a - b = c.</p>
<p>Kinda hard to understand w/o pictures, let me know if you still have trouble.</p>
<p>thanks for your help!</p>
<p>I actually got a different answer for the second question. </p>
<p>In the trapezoid on the left hand side, (clockwise, starting at the top b, the letters go b,c,a,b,b,a) there should be 360 degrees, because it is a quadrilateral. The 4 angles would be b, c+a, 2b, and a, so 360=3b+2a+c. Therefore, c would equal 360-2a-3b.</p>
<p>Cricketman you're right. We can't assume that the third angle will be angle c, we don't know that a + b + c = 180. This is a perfect example of a question that is classified as hard, but needs just one crucial step to make it easy. In this case, the crucial step was seeing the trapezoid.</p>
<p>Oh no, yeah you're right. Sorry about that.</p>