If two angles form a linear pair and the measure of the first angle is one-fifth the measure of the second angle, what is the measure of each angle?

Well, one angle has one share of the linear angle, and the other one has five shares. All together, they add up to six shares of the linear angle.

BUT ... a linear angle adds up to 180°. So each share must be (180°/6) = 30°.

The smaller one (one share) is 30°, and the larger one (5 shares) is 150°.

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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