Question

exterior angle theorem
an exterior is formed by extending any one side of the triangle.
an exterior is always equal to the sum of the two non - adjacent interior angles.
( mangle1=)
triangle angle sum theorem
the sum of the measures of the angles of a triangle is ( 180^{circ}).
( mangle a + mangle b + mangle c=)

Explanation:

Step1: Recall the Triangle Angle Sum Theorem

The Triangle Angle Sum Theorem states that for any triangle \(ABC\), the sum of the measures of its interior angles is \(180^{\circ}\). Mathematically, this is expressed as \(m\angle A + m\angle B + m\angle C=180^{\circ}\).

Step2: Recall the Exterior Angle Theorem

The Exterior Angle Theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. For the given triangle with exterior angle \(\angle1\) and non - adjacent interior angles \(\angle2\) and \(\angle3\), we have \(m\angle1=m\angle2 + m\angle3\).

Answer:

For the Triangle Angle Sum Theorem: \(m\angle A + m\angle B + m\angle C = 180^{\circ}\). For the Exterior Angle Theorem: \(m\angle1=m\angle2 + m\angle3\)