Question

In $\Delta XYZ$, side $\overline{XZ}$ is longer than side $\overline{YZ}$, which of the following statements is true?

• A. The measure of $\angle X$ is always less than the measure of $\angle Y$.
• B. The measure of $\angle X$ is always equal than the measure of $\angle Y$.
• C. The measure of $\angle X$ is always greater than the measure of $\angle Y$.
• D. The measure of $\angle X$ is sometimes less than the measure of $\angle Y$ and sometimes equal to the measure of $\angle Y$.
• E. The measure of $\angle X$ is sometimes greater than the measure of $\angle Y$ and sometimes equal to the measure of $\angle Y$.

Answer 1

The correct option is A The measure of $\angle X$ is always less than the measure of $\angle Y$.

Angles opposite to longer sides are larger.

Here $XZ>YZ$

Angle opposite to $XZ$ is $\angle Y$ and to $YZ$ is $X$

$\therefore \angle Y>\angle X$

So option $A$ is correct.