Question

In triangle XYZ, mZZ > mX + mY. Which must be true about ΔXYZ?

a) mX + mZ < 90°

b) mZY > 90°

c) X and Y are complementary

d) m2X + mY < 90°

Answer 1

The statement given about triangle XYZ, where mZ is greater than the sum of mX and mY, is fundamentally incorrect as it violates the triangle angle sum theorem which states that the sum of the angles in a triangle must be 180 degrees.

Step-by-step explanation:

In the scenario where in triangle XYZ, it is stated that mZ is greater than mX plus mY, this is an impossible situation for a triangle because the sum of two angles, in this case, mX and mY, should always be less than the measurement of the third angle, mZ, if mZ is the largest angle. The sum of all three angles in a triangle must always equal 180 degrees according to the triangle angle sum theorem. Therefore, none of the given options can be necessarily true based on the premise which is fallacious since it violates a fundamental property of triangles.