From the figure, we can deduce:
XY = x + 2
XZ = x + 1
Let's label the angles from the largest to smallest using the triangle inequality theorem.
The triangle inequality theorem is stated below:
XY + XZ > YZ
YZ + XZ > XY
XY + YZ > XZ
The theorem states that the sum of any two sides in a triangle is greater than the length of the third side.
From the triangle, the biggest angle will be the angle opposite the hypotenuse which is the largest side.
The larger angle will be the angle opposite the larger side.
The smallest angle will be the angle opposite the smallest side.
Largest side = XY
Larger side = XZ
Smallest side = YZ
Thus, we have:
• largest angle = ∠Z
,
• Larger angle = ∠Y
,
• Smallest angle = ∠X
ANSWER:
∠Z ; ∠Y ; ∠X