d)In the figure ,AB is the diameter . If angle ABP = 43° , angle BAQ = 65° find (i) angle PAB , (ii) angle PBQ
Answers
Answer:
Given,
AB is a diameter of a circle with the centre O and CD BA
∠BAC=20
o
Now,
(i)we know that the angle at the centre is twice the angle at the circumference subtended by the same arc.
Therefore,
∠BAC=20
o
∠BOC=20
o
×2
=40
o
(ii)Now,
∠DOA is the angle at the centre and ∠DCA is the angle at the circumference.
Therefore,
∠DOA=40
o
Now,
∠DOC=180
o
−∠DOA−∠BOC=180
o
−40
o
−40
o
=100
o
(iii)Now,
we know that the angle at the centre is twice the angle at the
circumference subtended by the same arc.
Therefore,
∠DAC=
2
1
∠DOC
=(
2
1
×100
o
)
=50
o
(iv) CD, BA and AC is the transversal
∴∠ACD=∠CAB=20
o
△ACD we have,
∠ADC+∠ACD+∠DAC=180
o
=>∠ADC+20
o
+50
o
=180
o
=>∠ADC=(180
o
−70
o
)
=110
Answer:
∠BAC=20
Step-by-step explanation: