। In the given figure, O is the centre of the circle. If LMPN = 6x° and ZPMN = 3x°, find the size of ZPQN. (Ans: 30°)
Answers
Answer:
In the given figure of the question, Q is the centre of the circle, and PM and PN are tangents from an external common point 'P'.
∠MPN=40
o
, to find ∠MQN
In □PMQN, ∠PMQ=∠PNQ=90
o
(Radius is ⊥ to tangent at point of contact from the centre)
∴∠PMQ+∠PNQ+∠MPN+∠MQN=360
o
(Sum of measures of interior angles of quadrilateral)
∴90
o
+90
o
+40
o
+∠MQN=360
o
∠MQN=360
o
−(90
o
+90
o
+40
o
)
=360
o
−220
o
=140
o
Step-by-step explanation:
6x+3x+90=180(angle made by diameter)
9x+90=180
x=10
3x=3*10=30
3x=pqn(angle made by two circumference angles sharing the same arc)
pqn=30