(i) \[\angle PQM+\angle NYZ=\angle PQR\] |
(ii) \[\angle MQR+XYN=\angle XYZ\] |
(iii) \[\angle PQM=2\angle PQR\] |
(iv) \[\angle XYZ=2\angle MQR\] |
A) (i) and (ii) only
B) (i) and (iv) only
C) (ii) and (iii) only
D) (i), (ii) and (iv) only
Correct Answer: D
Solution :
Given \[\angle PQR=\angle XYZ,\,\,\overrightarrow{QM}\] bisects\[\angle PQR\] and \[\overrightarrow{YN}\] bisects \[\angle \,\,XYZ\] respectively. \[\Rightarrow \angle PQM+\angle MQR=\angle XYN=\angle NYZ\] \[\Rightarrow \angle PQM+\angle MQR=\angle PQR\] is true. \[\angle MQR+\angle XYN=\angle XYZ\] is true \[\angle PQM=2\angle PQR\] is false as \[\angle PQM=\frac{1}{2}\angle PQR.\] \[\angle XYZ=2\angle MQR\] is true since \[2\angle MQR=\angle PQR=\angle XYZ\]. Hence (i), (ii) and (iv) are true.You need to login to perform this action.
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