Question

1. choose the correct answer.

which theorem or corollary could be used to prove the conjecture?
conjecture: ( mangle1 = mangle2 + mangle3 )
corollary 4.2b (measure of each angle of an equiangular triangle is ( 60^{circ} ))
third angles theorem
exterior angle theorem
corollary 4.2a (acute angles of a right triangle are complementary)

Explanation:

The Exterior Angle Theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In the given problem, \(\angle1\) is an exterior angle of the triangle, and \(\angle2\) and \(\angle3\) are the non - adjacent interior angles. So, \(m\angle1=m\angle2 + m\angle3\) can be proved using the Exterior Angle Theorem.
Corollary 4.2B is about equiangular triangles (all angles \(60^{\circ}\)), which is not relevant here. The Third Angles Theorem is used when two angles of one triangle are congruent to two angles of another triangle to show the third angles are congruent. Corollary 4.2A is about right - triangles (acute angles are complementary), which is also not relevant.

Answer:

Exterior Angle Theorem