The correct logical order of statements and reasons I, II, and III to complete the proof is:
Option: c. II, III , I
Definition of a straight line--
The definition of a straight line states that the angles that lie in a straight line is 180°.
Hence, from the following figure we have:
∠SQT=180°
Angle Addition Postulate--
It states that if the point lie in between the ray, then the sum of two angles formed with the help of the ray is equal to the larger angle.
i.e.
∠SQV+∠VQT=∠SQT
Substitution Property of Equality--
It states that if:
a=b and a=c then b=c
Hence we have:
∠SQV+∠VQT=180°
The most logical order of statements and reasons is II , III, I , Option C is the correct answer.
A straight line is a ray extended both sides such that the angle made is 180 degree
From the given figure
∠SQT=180° ( Straight Line ) ------------------------ (1)
Angle Addition Rule
When two angle is made of sum to two angles then it can be written as
∠SQV+∠VQT=∠SQT ----------------------------------- (2)
And by Substitution From equation 1 into 2
∠SQV+∠VQT=180°
Therefore the most logical order of statements and reasons is II , III, I , Option C is the correct answer.
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