Question

Does anyone know the answer to this problem?

Answer 1

Start with the fact that the sum of the angles in a triangle is 180°.
.. ∠A +∠B +∠C = 180
.. 65 +(3x -10) +(2x) = 180 . . . . . . substitute the given information
.. 55 +5x = 180 . . . . . . . . . . . . . . . collect terms
.. 11 +x = 36 . . . . . . . . . . . . . . . . . . divide by 5*
.. x = 25 . . . . . . . . . . . . . . . . . . . . . subtract 11

∠B = 3x -10 = 3*25 -10 = 65

∠C = 2x = 2*25 = 50
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In summary
.. x = 25
.. ∠B = 65°
.. ∠C = 50°

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* You could subtract 55, then divide by 5. You get the same answer either way. I find it easier to work with smaller numbers, and dividing all these values by 5 is fairly easy.