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Verified Answer :

zhduch

Since it is as a ratio of 14:31 there has to be a factor of something. Let's assume this factor as x. 

Therefore,

14x + 31x = 90 
45x = 90
x = 2

So we have a factor of two. Plug x back into the equation. 
The larger angle is 31 * 2 = 62 degrees.

bcalle

The ratio is 14:31 which is a total of 45 parts (14+31).
Divide 90 degrees by the 45 parts to find that each part is 2 degrees.
Multiply each part of the ratio by 2 to get 28:62.
The larger angle is 62 degrees