<p>ok, i posted the wrong link in the last one. ok, wat r all the ways of answering this and which is the fastest?</p>
<p>Why couldn’t you put all of these questions in the same thread? You’re flooding the forums.</p>
<p>ANSWER: (E) <CED</p>
<p>1) A careful way:</p>
<p>Rule: Quadrilateral CBAE’s internal angles add up to 360 degrees.</p>
<p>The quadrilateral has 2 90 degree angles (tangents and radii form 90 degree angles). This means that the remaining 2 angles of the quadrilateral, <ABC and <CEA, total 180 degrees. <CED is the supplement of <CEA, so both also total 180 degrees. So, <CED and <ABC are congruent in the same way…</p>
<p>A+B=Y
C+B=Y</p>
<p>…A equals to C</p>
<p>2) A faster way:</p>
<p>if <B has the same measure as <D, that would make the measure 45 degrees since the big triangle <BAD is a right triangle (90+45+45=180). That means the quadrilateral has a 45 degree angle and 2 90 degree angles, meaning the 4th angle is 360 - (45 + 90 + 90), or 135. The supplement is 45, which means there are 2 angles with the same measure as <ABD. That would then mean there are 2 correct answers, which can’t be, so the only other acute angle (<B is acute, so the angle with the same measure must also be acute) is the correct answer, <D or <CED</p>
<p>P.S. im sorry if you read this before i corrected my mistakes, i had a lot</p>
<p>Note that the big triangle ABD is a right triangle with angle D. The smaller triangle CDE is also right and shares angle D. Angles A + D = angles C + D, therefore angle B must equal angle E. Look through the answer choices to find the correct choice and your done.</p>
<p>^I did yankee belle’s way. You pretty much know that this is a similar triangle question. So, you find the similar triangles and walla! </p>
<p>Or you could just look at all the angles (not many), where some are clearly right, others are like 15 degrees, and others are obtuse. Normally I’d advise against this, but this figure seems to be drawn to scale.</p>
<p>If I had minutes to do this problem, and there was no other problem that I was unsure of AT ALL, I would consider doing the more complicated ways (above) to check. But honestly, that would never happen with me. There would generally be a better use of my time (which includes just resting).</p>
<p>i understand ur way yankee. crazy: i really tried understanding your ways but they were just not easy to comprehend. could some1 explain? if not thats fine too, when i have more time ill check it more in depth</p>
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<p>tangent and radius form 90 degree angles
4 sided shapes have angles whose measures add up to 360
straight lines are 180 degrees</p>
<p>x+y is 180 degrees</p>
<p>wow i get it now. how did u realize that?</p>
<p>well as soon as i labeled the 90’s i instantly knew the other 2 angles had measures that add up to 180 (common math). I then immediately looked for another pair of angles whose measures add up to 180, sharing 1 common angle (because G+B=C and Z+B=C means G=Z… its one of the properties taught in geometry class that becomes instinct). I did this because I started out with numbers (90 degrees) so I continued the problem using numbers (supplementary angles)</p>
<p>you could think about it like this: if you went the triangle route (yankee’s way), it was likely because you knew the measure of 1 of the 3 angles, and the congruence of 1 other angle (the one thats shared) so that you know the remaining angles are congruent. Using the quadrilateral would then warrant the knowledge of 2 of the 4, and the congruence of 1 other pair of angles</p>
<p><em>you dont have to understand this, this is just an explanation of 1 way of thinking</em></p>
<ol>
<li><p>Let C, E be fixed, then mentally vary A clockwise such that angle AEC approaches 90 from above (A goes to 9’o clock), D goes to infinity, (lines AED and BCD become parallel). Notice that only angles ABD and CED have the same behavior, both approach 90 from below.</p></li>
<li><p>This might be a repeat but, since angles BAD = ECD = 90 from tangency, triangle ABD is similar to CED and result follows.</p></li>
</ol>