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e-lub [12.9K]
2 years ago
6

two right triangles share a common side and have equal areas. the hypotenuse of the light green triangle is one of the legs of d

ark green triangle stacked on top of it. if the smallest angle of light green triangle is 18 degrees, what are the angles of the dark green triangle?
Mathematics
1 answer:
Alexandra [31]2 years ago
5 0

Answer:

the two angles of dark green triangle are 90 degrees, 72 degrees and 18 degrees.

Step-by-step explanation:

As dark green triangle is stacked on top of light green triangle and one side of dark green is sharing hypotenuse of light green, considering both have same area, mean same 1/2 base* height ,also one leg of both is same so its obvious that both heights and bases of triangles are same. Considering all the above facts both triangles are forming a square with common side as diagonal of square.

So, the angles of light green triangle are 90 , 18 and (180-90-18)=72 degrees

One angle of dark green is already 90 degrees , the other two combined with light green form 90 degrees (as both are side angles of square).

90-18=72

90-72=18

Hence the three angles of dark green triangle are 90,72 and 18.

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