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3 years ago

Please please please help !!

Mathematics

1 answer:

Lubov Fominskaja [6]3 years ago

6 0

Answer:

Step-by-step explanation:

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Can someone please help me with this asap ... Please and thank you

OLga [1]

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°

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3 years ago