Question

now solve the equation for ( mangle4 + mangle5 + mangle6 ).
( mangle4 + mangle5 + mangle6 = )

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\), but here \(\angle4\), \(\angle5\), \(\angle6\) form a straight - line (or a triangle's interior angles? Wait, no—if they are angles of a triangle, their sum is \(180^\circ\). Wait, actually, the sum of the interior angles of a triangle is \(180^{\circ}\). So if \(\angle4\), \(\angle5\), \(\angle6\) are the three interior angles of a triangle, then \(m\angle4 + m\angle5 + m\angle6=180\).

Step2: Confirm the sum

By the triangle angle - sum theorem, the sum of the measures of the interior angles of a triangle is \(180^{\circ}\). So regardless of the type of triangle, the sum of its three interior angles is \(180^{\circ}\).

Answer:

\(180\)