In the given question, Stuart is not correct.
The sum of all internal angles of a triangle is always equal to 180°.
Value of ∠1 = 65°(given)
Value of ∠7 = 55°(given)
Now let's look into Stuart's reasoning:
Step 1 : It is correct because according to angle sum property of triangle, ∠1 + ∠7 + ∠8 = 180°.
Step 2 : This step is wrong, because ∠4 and ∠8 are corresponding angles and not ∠12 and ∠8, so ∠4 = 60°.
Step 3 : This step is also wrong , ∠4 + ∠12 = 180°
So ∠12 = 180 - 60 = 120°
Hence, Stuart's value of ∠12 is not correct.
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