Let's observe the measurement of the angles of the following triangles and let's compare the length of the sides which one is smaller and whose one is greater.

(i) The given triangle is as shown below:

Given ∠A=60°, ∠C=30°, and the given triangle is a right-angled triangle, so ∠B=90°

To find the side BC is greater of side AB is greater.

In the given ΔABC,

∠A is opposite to side BC,

And ∠C is opposite to side AB

And from the given values, ∠A=60°is greater than ∠C=30°,

⇒ ∠A>∠C

We know in a triangle the shortest side is always opposite the smallest interior angle and the longest side is always opposite the largest interior angle.

⇒ side BC>side AB

Hence side BC is greater than side AB.

(ii) The given triangle is as shown below:

Given ∠X=60°, ∠Y=75°, ∠Z=45°

To find the side YZ is greater than which side.

In the given ΔXYZ,

∠X is opposite to side YZ,

And from the given values, ∠X=60°is greater than ∠Z=45°,

And ∠Z is opposite to side XY

⇒ ∠X>∠Z

We know in a triangle the shortest side is always opposite the smallest interior angle and the longest side is always opposite the largest interior angle.

⇒ side YZ>side XY

Hence side YZ is greater than side XY.

(iii) The given triangle is as shown below:

Given ∠Q=59°, ∠R=50°

To find which side is greater than which side

In the given ΔPQR

⇒ ∠Q>∠R

And from the given figure,

∠Q is opposite to side PR,

And ∠R is opposite to side PQ

We know in a triangle the shortest side is always opposite the smallest interior angle and the longest side is always opposite the largest interior angle.

⇒ side PR>side PQ

Hence side PR is greater than side PQ.