An angle is 20∘20 ∘ more than 44 times the given angle. If the two angles are supplementary, the smaller angle is equal to _________.
Question
An angle is 20° more than 44 times the given angle.
If the two angles are supplementary, the smaller angle is equal to _________.
Solution
Let's denote the smaller angle as x. According to the problem, the larger angle is 44x + 20 degrees.
Since the two angles are supplementary, their sum is 180 degrees. Therefore, we can write the equation:
x + 44x + 20 = 180
Solving this equation will give us the value of x, which is the smaller angle.
First, combine like terms:
45x + 20 = 180
Then, subtract 20 from both sides of the equation:
45x = 160
Finally, divide both sides by 45 to solve for x:
x = 160 / 45 ≈ 3.56 degrees
So, the smaller angle is approximately 3.56 degrees.
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