Question

Write the complement angle of: $ \dfrac{2}{5} $ of $ {70 ^\circ} $ .

Answer 1

Hint: First we have to define what the terms we need to solve the problem are.
Let us first define what is complement angle; which is the two angles are said to be complement if there exists a measure added to ninety degrees.
Also, the supplementary angle is said to be one-eighty degrees. Since in this question they asked us to find the complement angles only.

Complete step by step answer:
Since as per the complement angle definition the two angles are said to be complement only if their sum of the angles is ninety degrees.
But here there is only one angle which is $ \dfrac{2}{5} $ of $ {70 ^\circ} $ ; thus, we just need to subtract this angle concerning the $ {90 ^\circ} $ . For example, we know the value of $ {90 ^\circ} = x + y $ and here y is given as $ \dfrac{2}{5} $ of $ {70 ^\circ} $ .
So, we need to find the value of X; since $ \dfrac{2}{5} $ of $ {70 ^\circ} $ can be rewritten as $ \dfrac{2}{5} \times {70 ^\circ} = 2 \times {14 ^\circ} = {28 ^\circ} $ (by the help of multiplication and division we obtained this angle).
Hence Y is the twenty-eight degree and thus $ {90 ^\circ} = x + {28 ^\circ} $ .
Further solving this we get \[{90 ^\circ} = x + {28 ^\circ} \Rightarrow x = {62 ^\circ}\] (since sixty-two degrees is in the first quadrant).
Thus \[x = {62 ^\circ}\]which is the complement angle of $ \dfrac{2}{5} $ $ {70 ^\circ} $ .

Note: we are also able to find the supplementary angles for the respective question; which is the $ {180 ^\circ} $ measure of the given angles.
Thus, we get $ {180 ^\circ} = x + y $ where Y is $ \dfrac{2}{5} \times {70 ^\circ} = 2 \times {14 ^\circ} = {28 ^\circ} $ .
Hence, we get $ x = {162 ^\circ} $ (since one sixty-two degree is in the second quadrant).
Since there are only complements and supplementary angles; and zero degrees and three-sixty degrees are the same angles in the circle. Because both the degrees have the same starting and ending points on the degree tables.