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1) The three angle measures of a triangle are x/2, x/3 and x/6 degrees. What is the measure of the smallest angle?

2)Each pair of opposite sides of an octagon are parallel. We know three interior angles of the octagon are 115,125  and,135. What is the degree measure of the largest interior angle of the octagon?

3)What is the ratio of the number of degrees in the interior angle of a regular pentagon to the number of degrees in the interior angle of a regular hexagon?

Thanks!

Feb 5, 2019

#1
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1) If x/2, x/3, and x/6 are angle measures of a triangle, they must add up to 180.

x/2 + x/3 + x/6 = 180

Find the common denominator:

3x/6+2x/6 + x/6 = 180

Multiply both sides by 6:

3x+2x+x=1080

6x=1080,

x = 180

x/6, the smallest angle, is 30.

2) Correct me if I'm wrong, but isn't it just 135?

3) 108/120 = 9/10

Feb 5, 2019
#2
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For #2, 135 isn't correct but thank you for helping me solve 1 and 3. I did not look at #1 in the way that you showed.

Feb 5, 2019
#3
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I believe this might be the second one

The sum of the interior angles of an octagon = 135 * 8  = 1080°

So....the remaining two angles must sum to   1080 - 2(115 + 125 + 135)  = 330°

So....since the opposite sides are parallel.....the largest remaining angles each measure 330/2 = 165°   Feb 6, 2019