Angles in a triangle

In a triangle, the first angle measures a number plus 45°, and the second angle is 30° less than the first angle. The third angle is two times the number more than the first angle. What are the measurements of each angle of the triangle?

Correct answer:

α =  63.75 °
β =  33.75 °
γ =  82.5 °

Step-by-step explanation:

α=2x+45 β=α30=2x+4530=2x+15 γ=2x+α=2x+2x+45=4x+45 α+β+γ=180  2x+45+2x+15+(4x+45)=180  2 x+45+2 x+15+(4 x+45)=180  8x=75  x=875=9.375  x=875=9.375  α=2 x+45=2 9.375+45=63.75=63°45
β=2 x+15=2 9.375+15=33.75=33°45
γ=4 x+45=4 9.375+45=2165=82.5=82.5=82°30   Verifying Solution:  s1=α+β+γ=63.75+33.75+82.5=180 

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