From the Right angle triangle whose sides are 4 and 3 then Hypotense = 5

Form the Right angle triangle whose one side is 12 and hypotense is 13 then side = 5


So clearly the two side are equal making it into an isosceles triangle .

So 55 + 55 + x = 180

x = 70

Ans . D

Please excuse me for this ridiculously stupid question, but how do you know that it's:
55 + 55 + x = 180
and not:
55 + 2x = 180

(meaning: how do you know it's not the other 2 angles (the x and unmarked angle) that are the 2 identical angles?)

Thanks

one side = 5

other side = 5

So x = (180 - 110) = 70

Answer - D

@meliha, sides opposite to equal angles are equal, so they are equal (opposite to 55 degrees angle), but we don't know yet about x, so we can't assume x is equal to another angle.
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Looked up properties of isoceles triangle last night (after posting my question) and discovered answer to my own question. My understanding is that side the left and right sides are equal (both = 5), then that means the left and right bottom angles are also equal (property of isoc tri), which means that there must be 2 55 deg angles (instead of 2 other sized angles + 55.

55 + 55 + x = 180
x = 180 - 110
x = 70

Got it now, thanks.

Soooo many equations and formulas to memorize/remember...

In this question,
there are two "Pythagoras triplets" involved.
3-4-5 and 5-12-13
Looking at the dimensions of two right triangles, we can conclude that both the arms of angle "x" are of 5 units of length!

Thus it is an isoseles triangle. So other angle is same as 55 degrees
Thus, x = 180-55-55 = 70 degrees!

The shaded triangle is an isosceles triangles because

both sides are calculated 5 per Pythagoras theorem

Both angles must be same = 55

x = 180 - 2*55 = 70

Answer = D

We see that the right triangle on the left is a 3-4-5 right triangle, and the right triangle on the right is a 5-12-13 right triangle. Thus, the middle triangle has two sides equal to 5. Since one of those sides is opposite a 55-degree angle, the other side must also be opposite a 55-degree angle. Thus, x is:

180 - (55 + 55) = 70.

Answer: D
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