Question

if 1/4 of the supplementary of an angle is 19 more than 1/3 of the complementary of that angle. Find the angle​

Answer 1

Answer: 48°

Step-by-step explanation:

We can put a variable $x$ as the angle in question. First we can draw out the supplementary angle. I know that $x$ must be acute because it can be a complementary angle. So, the smaller angle will be $x$, and the larger angle will be 180°-x.

Next, we can draw the complementary angles. One angle will be x and the other, 90-x.

Now we can go back to the equation. The problem tells me that 1/4 of 180-x is 19 more than 1/3 of 90-x. I can make an equation like this: $\frac{1}{4} (180-x)=\frac{1}{3} (90-x)+19$. This can be simplified by expanding the parentheses and multiplying the fractions: $45-\frac{1}{4} x=30-\frac{1}{3} x+19$. Now, I can solve the problem. First, we can group like values together. I moved 45 and 30 together as well as the x values: $45-30=\frac{1}{4} x-\frac{1}{3} x+19$. I can then

compute the rest to get something like this: $15-19=-\frac{1}{12} x\\-4=-\frac{1}{12} x\\x=-48$. However this answer gives us a solution that is negative, and we know that values of angles cannot be negative. Therefore, we should make x into it's positive counterpart, 48.

Now, we can check our answer. 180-48=132. 132/4=33. 90-48=42. 42/3=14. We can subtract 14 from 33 to get 19, so our answer is correct.