Question

the measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.
if...
diagram of a triangle with angle 1, 2, 3
then... ( mangle 1 = mangle 2 + mangle 3 )
explore the triangle exterior angle theorem by moving the vertices of the triangle.
image of triangle abc with angles 120° at a, 90° at c, 30° at b

Explanation:

Step1: Identify the two remote interior angles

In triangle \(ABC\), for the exterior angle at \(A\) (which is \(120^\circ\)), the two remote interior angles are \(\angle B\) and \(\angle C\). We know \(m\angle B = 30^\circ\) and \(m\angle C=90^\circ\).

Step2: Calculate the sum of the two remote interior angles

Sum of \(m\angle B\) and \(m\angle C\) is \(m\angle B + m\angle C=30^\circ + 90^\circ = 120^\circ\), which is equal to the measure of the exterior angle at \(A\) ( \(120^\circ\) ). This verifies the Triangle Exterior Angle Theorem.

Answer:

The Triangle Exterior Angle Theorem is verified as \(30^\circ+90^\circ = 120^\circ\), so the measure of the exterior angle at \(A\) equals the sum of the measures of its two remote interior angles (\(\angle B\) and \(\angle C\)).