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(i) The given triangle with naming is as shown below:

Given ∠ACB=55°, ∠BAC=40°

To find the angle, i.e., ∠ABC=x°

Now Consider the ΔABC,

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

So in this case,

∠ABC+∠BAC+∠ACB=180°

Substituting the values, we get

x°+40°+55°=180°

⇒ x°=180°-40°-55°

⇒ x°=85°

So the measurement of unknown angle in this triangle is 85°.

(ii) The given triangle with naming is as shown below:

Given ∠ACB=30°, ∠BAC=30°

To find the angle, i.e., ∠ABC=x°

Now Consider the ΔABC,

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

So in this case,

∠ABC+∠BAC+∠ACB=180°

Substituting the values, we get

x°+30°+30°=180°

⇒ x°=180°-30°-30°

⇒ x°=120°

So the measurement of unknown angle in this triangle is 120°.

(iii) The given triangle with naming is as shown below:

Given triangle is a right-angled triangle, so ∠ABC=90° and also given ∠ACB=30°

To find the angle, i.e., ∠BAC=x°

Now Consider the ΔABC,

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

So in this case,

∠ABC+∠BAC+∠ACB=180°

Substituting the values, we get

90°+x°+30°=180°

⇒ x°=180°-90°-30°

⇒ x°=60°

So the measurement of unknown angle in this triangle is 60°.