Since AC is Extended through point C to point D, and BE is drawn to AC, an equation that is always true is: 4) m∠7 = m∠3 + m∠2
In Mathematics and Euclidean Geometry, the exterior angle theorem or postulate states that the measure of an exterior angle in a triangle is always equal in magnitude (size) to the sum of the measures of the two remote or opposite interior angles of that triangle.
By applying the exterior angle theorem, we can reasonably infer and logically deduce that the sum of the measure of the two interior remote or opposite angles in triangle ABC is equal to the measure of angle 7 (m∠7);
m∠2 + m∠3 + m∠4 = 180 (supplementary angles add up to 180 degrees.)
m∠2 + m∠3 + m∠4 = m∠7 + m∠4
m∠7 = m∠3 + m∠2