A Cute Triangle

[afashoro]

What is the degree measure of angle a?
(1) b + c = 287 degrees
(2) d + e = 269 degrees

I understand how to solve this but for some reason I'm struggling to figure out a quick way to solve this problem in =< 2 minutes.

[gokul_nair1984]

Please post the complete problem (with figure if possible)

[mschwrtz]

There may be better ways--feel free to jump in with any expertise--but you can go to an image-hosting site like postimage.org to, well, post images.

[sivai87]

Hi.. Please find the image below.. Help needed on this problem.. Thanks in advacne..



Kind Regards,
Sivai

[jnelson0612]

sival,
I think that the quickest and easiest way to do this is to rephrase. The question asks the degree measure of angle a, but since we know that opposite angles are equal it could also be asking the degree measure of angle e.

We also know that e + f + g = 180, so e=180 - (f+g). In other words, if I know (f+g) I can determine e, which is equal to a. So my new rephrased question is what is (f+g)? Or what is the degree value of angle e? Either will get me to the degree value of angle a.

1) b+c = 287 degrees. I know that (b+f) and (c+g) each equal 180 because they are straight lines. Rewrite as (b+c) + (f+g) = 360. Sub 287 in for (b+c) and you have 287 + (f+g) = 360. Thus, (f+g) = 73. Sufficient.

2) d+e = 289 degrees. This is not helpful. You could plug in different values for d and e into the diagram. For example, I could say:
d=150
e=139
f=30
g=11

or I could say:
d=155
e=134
f=25
g=21

Either of these scenarios fits all geometric rules; thus, this information does not help us determine the degree value of angle a. Insufficient.

[sivai87]

Thanks Jamie

[jnelson0612]

My pleasure sival.