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geometry-missing angles

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Junior | Next Rank: 30 Posts
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geometry-missing angles

by knowledgeisatreasure » Sat Aug 15, 2009 9:59 am
Hi,

would you please help me with this question:

In the figure above, what is the value of x?
it is given 3 triangles: 2 are right angle triangles, the middle is not.
the sides of the first right triangle is: a^2 + 12^2 = 13^2 (a=1)
the sides of the second right triangle is: 3^2 + 4^2 = c^2 (c= 5)

I'm including a print screen shot to illustrate the figures. Sorry for the confusion.

My approach was first to use the a^2+b^2= c^2 formula. I found the missing sides, but when it comes to the missing angle (x) I didn't know what to do, given the opposite angle is 55 degrees.

thank you
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by Morgoth » Sat Aug 15, 2009 11:25 am
Remember the following by heart:

3-4-5
5-12-13

The above examples are known as pythagorean triplets. These are most common examples of triplets tested on GMAT.

if you look at the figure now, you can easily know that the other 2 sides will be 5,

since one angle is 55, the other unknown angle will also be 55, because, the two angles have equal sides i.e. 5

x + 55 + 55 = 180

x = 180-110 = 70

Hope this helps.
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Junior | Next Rank: 30 Posts
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by knowledgeisatreasure » Sat Aug 15, 2009 11:32 am
thanks a lot
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Junior | Next Rank: 30 Posts
Posts: 18
Joined: Thu Jun 25, 2009 7:07 pm

by knowledgeisatreasure » Sun Aug 16, 2009 10:48 am
I forgot to mention why I was getting one side of the triangle was 5 and the other was 1 (instead of 5) simply because my basic math was wrong:

a^2 + 12^2 = 13^2 is not equal to a^2= 13^2 - 12 ^2 (this way I will get
a ^2 = 1 ^2 equals to a = 1 (THIS IS WRONG!!!!)

I should have done this instead: a^2 + 144 = 169 ; a^2 = 25 ; a = 5

as the previous response illustrated that 2 sides are equal means that 2 angles should be the same and angle X is 70 degrees.

Once again thank you for your response.

what does the first 2 lines mean exactly ?? that you said i have to know by heart.
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