Any time you are faced with a problem like this you want to stop and ask yourself... "would it be easier for me to see this with separate triangles?". Certainly it would be. The other thing your should identify here is the use of the triangle angle sum theorem. This theorem was devised many years ago and basically states that all three angles in a triangle add to 180 (supplementary).

The strategy here woul be to use this theorem to determine that the smallest angle has a third angle of 17. If you can see that the triangles overlap then you can determine the second triangle has a third angle of 28. To determine the small non overlapping space you could subtract 17 from 28. The largest triangle has a third angle of 40 degrees however 28 degrees is overlapping from the second triangle.

3 years ago

## Answered By Charles S

Any time you are faced with a problem like this you want to stop and ask yourself... "would it be easier for me to see this with separate triangles?". Certainly it would be. The other thing your should identify here is the use of the triangle angle sum theorem. This theorem was devised many years ago and basically states that all three angles in a triangle add to 180 (supplementary).

The strategy here woul be to use this theorem to determine that the smallest angle has a third angle of 17. If you can see that the triangles overlap then you can determine the second triangle has a third angle of 28. To determine the small non overlapping space you could subtract 17 from 28. The largest triangle has a third angle of 40 degrees however 28 degrees is overlapping from the second triangle.

The answer here is 12 degrees for x.

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