Question

Consider triangle WXY... which statement about the angles is true?

Angle W is greater than angle Y.
Angle Y is the largest angle.
Angle X is smaller than angle W.
Angle W is the smallest angle.

Answer 1

1) Angle W is greater than angle  = yes since it's opposed to a larger side

2) Angle Y is the largest angle. = Wrong

3) Angle X is smaller than angle = Wrong.

4) Angle W is the smallest angle. =Wrong


Take it as a principle, the largest the angle the largest the opposed side & vice versa

Answer 2

Answer:  The correct option is (A) Angle W is greater than angle Y.

Step-by-step explanation:  Given that the measures of the three sides of a triangle XYZ are as follows:

XY = 10 units,

WY = 14 units,

WX = 5 units.

We are to select the correct statements regarding the angles of ΔXYZ.

Writing the lengths of the sides in ascending order, we have

$5<10<14\\\\\Rightarrow WX<XY<WY~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Since the angle opposite to a smaller side of a triangle is smaller, so from inequality (i), we get

$WX<XY<WY\\\\\Rightarrow \angle Y<\angle W<\angle X\\\\\Rightarrow \angle X>\angle W>\angle Y.$

Option (A) is "Angle W is greater than angle Y".

This option is correct, because we have  ∠W > ∠Y.

Option (B) is "Angle Y is the largest angle".

This is incorrect because ∠X is the largest angle.

Option (C) is "Angle X is smaller than angle W"

This is incorrect because ∠X is the largest.

Option (D) is  "Angle W is the smallest angle".

This is incorrect because ∠Y is the smallest.

Thus, (A) is the correct option.