What is the reason for step 3 in the two column proof below 1. ZPQR is a right angle
1. Given
2. MZPQR = 90°
2. Definition of Right Angle
3. m_PQS + MZSQR = m_PQR
3. ?
4. MZPQS + m_SQR = 90°
4. Substitution Property of Equality
5. ZPQS and 2SQR are complementary 5. Definition of Complementary Angles
Definition of Congruent Angles
Vertical Angles Congruence Theorem
Angle Addition Postulate
Definition of Angle Bisector

The correct option is;

Angle Addition Postulate;

Step-by-step explanation:

The given two column proof can be presented as follows;

Statement                                                Reason

1. ∠PQR is a right angle                           Given

2. m∠PQR = 90°                                      Definition of Right Angle

3. m∠PQS + m∠SQR = m∠PQR               Angle Addition Postulate

4. m∠PQS + m∠SQR = 90°                       Substitution property of equality

5. ∠PQS and ∠SQR are complementary Definition of complementary angles

Given that the angle m∠PQR has angles m∠PQS and m∠SQR arranged adjacent to each other while sharing the same boundary segment, QS we have by the angle addition postulate;

m∠PQR is the sum of the angles m∠PQS and m∠SQR, therefore;

m∠PQR = m∠PQS + m∠SQR = 90°.