Question

1. choose the correct answer. which theorem or corollary could be used to prove the conjecture? conjecture: ( mangle1 ) is not greater than or equal to ( 90^{circ} ). corollary 4.2a (acute angles of a right triangle are complementary) corollary 4.2c (triangle can have no more than one right angle or obtuse angle) exterior angle theorem corollary 4.2b (measure of each angle of an equiangular triangle is ( 60^{circ} ))

Explanation:

• Corollary 4.2A: This is about acute angles in a right - triangle. But the conjecture is not about a right - triangle context.
• Corollary 4.2C: A triangle can have at most one right or obtuse angle. If \(m\angle1\geq90^{\circ}\), then the sum of the three angles of the triangle would exceed \(180^{\circ}\) (since the other two angles are positive).
• Exterior Angle Theorem: Relates an exterior angle of a triangle to the sum of the two non - adjacent interior angles. Not relevant to the given conjecture.
• Corollary 4.2B: Applies to equiangular triangles. The given triangle is not equiangular.

Answer:

Corollary 4.2C (triangle can have no more than one right angle or obtuse angle)