Answer:
Step-by-step explanation:
From the question given in the picture,
a). Since, NR bisects a straight angle ∠MNP,
∠MNR ≅ ∠PNR
m∠MNR + m∠PNR = 180°
2(m∠MNR) = 180°
m∠MNR = 90°
Therefore, ∠MNR and ∠PNR are the right angles.
Since, QN divides ∠MNR in two parts,
Therefore, ∠QNR will be an acute angle (less than 90°).
∠MNR + ∠SNR = ∠MNS
90° + ∠SNR = ∠MNS
Therefore, m∠MNS will be more than 90°.
∠MNS will be an obtuse angle (greater than 90°).
(b). Since, NR divides ∠MNP and ∠QNS,
∠MNR ≅ ∠PNR
∠QNR ≅ ∠SNR
∠MNQ ≅ ∠PNS
(c). m∠MNR = 90°
Since, NR bisects ∠QNS,
∠QNR ≅ ∠RNS
m∠QNR = m∠RNS = 30°
m∠QNR + m∠RNS = 30° + 30°
m∠QNR + m∠RNS = 60°
m∠QNS = 60° [Since, m∠QNS = m∠QNR + m∠RNS]
m∠QNP = m∠QNS + m∠SNP
m∠QNP = m∠QNS + (m∠PNR - m∠SNR)
m∠QNP = 60° + (90° - 30°) = 120°
CHECKS