Let’s write the value of x in each of the following figure.

The given figure is as shown below:

Given ∠PRQ = 60°, ∠QPR = 50°, ∠QST = 30°

To find the exterior angle, i.e., ext ∠STR = x°

Now consider ΔPQR

We know in a triangle the sum of all three interior angles is equal to 180°.

So in this case,

∠PRQ + ∠PQR + ∠QPR = 180°.

Substituting the values, we get

60° + ∠PQR + 50° = 180°

⇒ ∠ PQR = 180° - 60° - 50°

⇒ ∠ PQR = 70°

Now PQS is a straight line, so

∠PQS = 180°

⇒ ∠PQR + ∠SQT = 180°

Now substituting the values, we get

⇒ 70° + ∠SQT = 180°

⇒ ∠SQT = 180° - 70°

⇒ ∠SQT = 110°

From figure consider ΔQST, so

In this triangle ∠STR is exterior angle,

And we know the measure of any exterior angle of a triangle is equal to the sum of the measures of its two interior opposite angles.

Hence ∠STR = ∠QST + ∠SQT

Substituting the values, we get

⇒∠STR = 30° + 110°

⇒∠STR = 140°

So the measurement of exterior angle in the given figure is 140°.