Let me re-phrase this question: a total of 180 cheese slices are divided among Leia and Luke such that for every 7 slices that Leia gets, Luke gets 8. How many slices does Leia get? Lets verify that the questions are the same: # slices that Leia gets / # slices that Luke gets = 7/8 (that is the ratio of the angles) # slices Leia gets + # slices that Luke gets = 180 (this is the sum of the two angles) We know that for every 7 slices that Leia gets, Luke gets 8 slices. So, out of a total of 15 slices, Leia gets 7 and Luke gets 8. We need to find out how many slices Leia gets among the 180 slices. To do that, we need to figure out how many of such bunches of 15 slices are present in 180 slices. Lets call a bunch of 15 slices, a pack of slices. How many such packs exist in 180 slices? That would be total number of slices divided by number of slices in a pack = 180 / 15 = 12. In each pack, Leia gets 7 slices and Luke gets 8 slices. So, in the 12 packs, Leia gets 12*7 = 84 slices. To keep it simple, I have tried doing this without using any Mathematics concepts.

Let the smaller angle be x \text{ and the larger angle be } y . Since the ratio is 7: 8, it means that \frac{x}{y} = \frac{7}{8} . Since the sum of the angle is 180^\circ , we also have x + y = 180^\circ . Now, we have a system of equations with two variables that we will solve using the method of substitution. The first equation is x - \frac{7}{8}y = 0 . We get the first equation by multiplying both sides of \frac{x}{y} = \frac{7}{8} by y . Now, substitute the value of x in the second equation to get \frac{7}{8} y + y = 180^\circ \implies \frac{15}{8} y = 180^\circ \implies y = \frac{8}{15} 180^\circ \implies y = 96^\circ . Therefore, the smaller angle is x = \frac{7}{8} 96^\circ = 84^\circ . If you don't understand any step here, you can simply add your comment on which particular step was difficult to follow and a more detailed explanation will be provided.