Question

A farmer is building three triangular pens such that  . If UV > US > SR, which is a true statement?

m∠UTV = m∠UTS = m∠STR
m∠UTV < m∠UTS < m∠STR
m∠UTS  > m∠UTV > m∠STR
m∠UTV > m∠UTS > m∠STR

Answer 1

Statement 4 is correct .i.e., m∠UTV > m∠UTS > m∠STR

Explanation:

Given: UV > US > SR.

To find: Correct Statement

We use property of triangle which states that In a triangle, the side opposite to larger angle is longer.

So, UV > US

⇒ m∠UTV > m∠UTS ....................... (1)

Also, since US > SR,

⇒ m∠UTS > m∠STR ............................ (2)

Thus from equation (1) & (2), we get

m∠UTV > m∠UTS > m∠STR

Therefore, Statement 4 is correct .i.e., m∠UTV > m∠UTS > m∠STR

Answer 2

m∠UTV > m∠UTS > m∠STR

Explanation:

We have been given that UV > US > SR.

In a triangle, the side opposite to larger angle is longer.

Therefore, UV > US gives m∠UTV > m∠UTS.

Also, since US > SR,

It gives that

m∠UTS > m∠STR

Hence, m∠UTV > m∠UTS > m∠STR