Hi, I am struggling to understand these kind of questions.

Your first thought here should be *“Is x 90 degrees?”* You can only compare the quantities if you know the value of x.

Now, we can’t find the measure of the angle traditionally because the other angles aren’t given. But we can check if it’s a right-angled triangle using Pythagoras theorem.

If the triangle is a right angled triangle, then according to Pythagoras theorem (or the inverse of it - not sure which one), the sum of the squares of the lengths of the smaller sides will be equal to the square of the length of the bigger one (the hypotenuse).

So you need to find if (11)^2+(5)^2 is equal to (13)^2.

On calculating you’ll find that it isn’t - so the triangle is not a right angled triangle. There’s no other way to determine the measure of the angle, so the answer should be **D. Cannot be determined.**

thank you so much.

first assume the nearest right angle triangle you can create. that would be the classic 5-12-13 triangle. therefore if the 11 in the question above would be 12, then angle x would be 90. now you start reducing the side 12 to 11, you will see that angle x will increase in value. Hence, since 11 is < 12 , x will be > 90.

therefore answer shall be A.