In a right angled triangle, what are possible values of the other two angles?

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 $90^\circ$. The sum of all angles in any triangle is always $180^\circ$.

Step 2: Calculate the sum of the other two angles

Since one angle is $90^\circ$, the sum of the other two angles must be $180^\circ - 90^\circ = 90^\circ$. 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 $0^\circ$. Also, since the sum of the other two angles is $90^\circ$, neither angle can be $90^\circ$ or greater. Therefore, each of the other two angles must be acute, meaning they are between $0^\circ$ and $90^\circ$.

Step 4: Illustrate possible values

There are infinitely many possible pairs of angles that sum to $90^\circ$. For example, if one angle is $30^\circ$, the other is $60^\circ$. If one angle is $45^\circ$, the other is also $45^\circ$ (an isosceles right-angled triangle).

More from this chapter

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