Question

What is the largest angle of the triangle?

a. X
b. Y
c. Z
d. P

Answer 1

Hint: We will use the triangle inequality theorem to find the largest angle in the given triangle. We will search for the greatest sides and the angle opposite to the greatest side will be the greatest angle of that triangle.

Complete step-by-step answer:
It is given in the question that we have to find out the largest angle of the triangle given.

For this, we will use the triangle inequality theorem. According to the triangle inequality theorem, in a triangle, the largest angle is the one opposite to the longest side of the triangle.
We will arrange the given the sides of the triangle in an ascending order of their length, we will get,
7< 10< 20
We know that the angle opposite to the longest side will have the largest value. Therefore, from the figure, we can say that,
$\angle Y<\angle X<\angle Z$
Therefore, in triangle XYZ, we have the greatest angle as angle Z.
Thus, option (c) is the correct answer.

Note: It is noted that many students assume that, according to the inequality theorem, in a triangle, the shortest angle is the one across the longest side of that triangle and as a result, they may choose angle X as the answer, but this is not correct. Thus, it is highly recommended that the students revise the triangle inequality theorem.