Question

find the possible values for $mangle1$.
$56 < mangle1 < 180$
$mangle1 = 124$
$0 < mangle1 < 56$
$56 < mangle1 < 90$

Explanation:

Step1: Use the exterior angle property

An exterior angle of a triangle is greater than either of the non - adjacent interior angles. Here, \(\angle1\) is an exterior angle of the triangle. The non - adjacent interior angle is \(56^{\circ}\). Also, an angle in a plane (exterior angle in this case) must satisfy \(0^{\circ}56^{\circ}\) (from the exterior angle property) and \(m\angle1 < 180^{\circ}\) (angle in a plane), we get \(56 < m\angle1<180\).

Answer:

\(56 < m\angle1 < 180\)