Question

How do I know what the measure is of the third angle?

Answer 1

The sum of the inner angles of any triangle is always 180º

So if for example, you have a triangle with angles ∠1, ∠2 and ∠3 and you add them, the result must be 180º:

$\angle1+\angle2+\angle3=180º$

This is useful when you know the measure only two inner angles.

To calculate the measure of the third one you just have to subtract the known angles to 180º:

$\begin{gathered} \angle1+\angle2+\angle3=180º \\ \angle3=180º-(\angle1+\angle2) \end{gathered}$

In this exercise, you have the angles

∠1= 23º

∠2= 98º

To determine the measure of the third angle you have to proceed as follows:

$\begin{gathered} 23º+98º+\angle3=180º \\ 121º+\angle3=180º \\ \angle3=180º-121º \\ \angle3=59º \end{gathered}$

The third angle measures 59º