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# Building a Ski-ramp

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Write an inequality in the variable x for the degree measure of the smallest angle of a triangle given that the degree measure of the smallest angle is at most 30 degrees

diagram
top angle x+8
bottom left x
right angle has ?

https://brainmass.com/math/triangles/building-a-ski-ramp-373419

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The third angle in the given triangle = 180° - (x + x + 8) = 180° - 2x - 8° = 172° - 2x
We know that for any positive value of x, x < x + 8
Now consider x and 172 - 2x
Depending upon the value of x, either x becomes the smallest angle or 172 - 2x becomes the smallest angle
(a) Assuming x to be the smallest angle, the inequality is obviously 0 < x ≤ 30
(b) Assuming 172 - 2x to be the smallest angle, the inequality is 0 < 172 - 2x ≤ 30
172 - 2x > 0
172 > 2x
2x < 172
x < 86
Again, 142 ≤ 2x
2x ≥ 142
x ≥ 71
So, assuming 172 - 2x to be the smallest angle, the inequality is 71 ≤ x < 86
Answer: {x | 0 < x ≤ 30 or 71 ≤ x < 86}

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