In a right angled triangle, what are possible values of the other two angles?
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Step-by-Step Solution
Step 1: Understand the properties of a right-angled triangle
A right-angled triangle is a triangle in which one of the angles is exactly 90∘. The sum of all angles in any triangle is always 180∘.
Step 2: Calculate the sum of the other two angles
Since one angle is 90∘, the sum of the other two angles must be 180∘−90∘=90∘. Let's call these two angles B and C.
Step 3: Determine the possible range for each angle
For a triangle to exist, each angle must be greater than 0∘. Also, since the sum of the other two angles is 90∘, neither angle can be 90∘ or greater. Therefore, each of the other two angles must be acute, meaning they are between 0∘ and 90∘.
Step 4: Illustrate possible values
There are infinitely many possible pairs of angles that sum to 90∘. For example, if one angle is 30∘, the other is 60∘. If one angle is 45∘, the other is also 45∘ (an isosceles right-angled triangle).