- Use the triangle angle sum property to find missing angles
triangle angle sum theorem
The sum of the interior angles of a triangle is always [latex]180^\circ[/latex]:
[latex]A + B + C = 180^\circ[/latex]
Find the missing angle in a triangle where [latex]A = 35^\circ[/latex] and [latex]B = 75^\circ[/latex].
[latex]\begin{align} A + B + C &= 180^\circ \\ 35^\circ + 75^\circ + C &= 180^\circ \\ 110^\circ + C &= 180^\circ \\ C &= 70^\circ \end{align}[/latex]
Find the missing angle in a right triangle if [latex]A = 28^\circ[/latex].
Because one angle is [latex]90^\circ[/latex], [latex]A + B = 90^\circ[/latex]
[latex]\begin{align} 28^\circ + B &= 90^\circ \\ B &= 62^\circ \end{align}[/latex]
Right triangles are especially easy — the two acute angles always add up to [latex]90^\circ[/latex].