Question

In triangle XYZ, XY = 3, YZ = 5, and XZ = 4. Based on this information, which is

accurate?
A The measure of ZX is the greatest of the three angles.
B The measure of ZX is the least of the three angles.
C The measure of ZY is the greatest of the three angles.
D The measure of all angles are the same.

Answer 1

The answer would be C, (The measure of ZY is the greatest of the three angles.)

Explanation:

YX=3, ZY=5, ZX= 4

(YX)≤(ZX)≤(ZY)

or

3≤4≤5

Answer 2

A) The measure of ∠X is the greatest of the three angles.

Explanation:

In a triangle:

• The angle with the greatest measure is opposite the longest side.
• The angle with the least measure is opposite the shortest side.

Therefore, in triangle XYZ, where XY = 3, YZ = 5 and XZ = 4:

• The measure of angle X is the greatest of the three angles since it is opposite the longest side YZ.
• The measure of angle Z is the least of the three angles since it is opposite the shortest side XY.

The measure of the all the angles cannot be the same since the three side lengths are different.