Question

The sum of two angles is 90 degrees. The angles are in the ratio 2:3. Find the measure of each angle.

Answer 1

Hint: Assume a constant multiplying factor for the ratio most likely a variable like and then proceed with the conditions given in the question.

Complete step-by-step answer:
As this a question of ratio proportion we assume a constant multiplying factor for the ratio. Let us take the factor to be $x$.
Therefore, we can say that one of the angles would be $2x$ and the other angle would be $3x$.
We know that the sum of the angles given above is 90 degrees. Applying the same condition, we get
$
  2x + 3x = 90 \\
  5x = 90 \\
  x = 18 \\
$
Therefore, the constant multiplying factor is 18.
Therefore, the value of one angle would be $2x$ = $2 \times 18 = 36$ degrees and the value of the other angle would be $3x$ = $3 \times 18 = 54$ degrees.
Thus, the two angles which are in the ratio of 2:3 and whose sum is 90 degrees is 36 degrees and 54 degrees respectively.

Note: The only thing to keep in mind is to read the question properly. In many questions the conditions might not be straightforward. They might ask us to find the average value of the two angles or the difference of the two angles. So, the question can be asked in a different possible way.