Short Answer C
Nice little problem. The catch is that alpha and beta both add up to 90 degrees.
Here's why.
α + β + right angle = 180° All triangles have 180° A right and = 90°.
α + β + 90 = 180 Right angles are 90° Now subtract 90° from both sides
α + β = 180 - 90
α + β = 90
Now all you have to do is put in the x values for alpha and beta and equate them to 90
5x/3 + 20 + 2x/3 + 14 = 90 Collect the light terms.
5x/3 + 2x/3 + 20 + 14 = 90
7x/3 + 34 = 90 Subtract 24 from both sides.
7x/3 = 90 - 34
7x/3 = 56 Multiply by sides by 3
7x = 3*56
7x = 168 Divide by 7
x = 168/7
x = 24
That's not quite the answer
The question wants alpha.
α = 5x / 3 + 20
α = 5*24/3 + 20
α = 120/3 + 20
α = 40 + 20
α = 60
Answer C <<<<<<
Answer: There is sufficient evidence to support the claim that the bags are under-filled.
Step-by-step explanation:
Since we have given that

Sample mean = 411
Standard deviation = 20
n = 9
So, the test statistic value is given by

At 0.025 level of significance,
critical value z = -2.306
since -2.306<-1.05
so, we will reject the null hypothesis.
Yes, there is sufficient evidence to support the claim that the bags are underfilled.
To simplify this you simply subtract 187 from 2431 (unless of course that is not intended to be a subtraction sign, in which case the number as it exists is in its simplest form).