Which angle has a measure equal to the sum of the m∠SQR and the m∠QRS?

Answer: 180° - m∠RSQ

Proof:

Refer to the diagram shown below.

Let

x = m∠SQR

y = m∠QRS

z = m∠RSQ

w = the external angle (supplement) of m∠RSQ

Because the sum of angles in a triangle is 180°, therefore

x + y + z = 180°

x + y = 180° - z

That is,

m∠SQR + m∠QRS = 180° - z (1)

Because the sum of angles on one side of straight line is 180°, therefore

w + z = 180°

or

w = 180° - m∠RSQ (2)

Equate equations (1) and (2) to obtain

m∠SQR + m∠QRS = completes∠RSQ

This completes the proof.

The answer would be c rsc