In the given figure ABCD is a cyclic quadrilateral is centre of the circle and a:b = 2:5, the value of x
is
a 20 degree
b 25 degree
c. 35 degree
b. 30 degree
Answers
Step-by-step explanation:
CBD&∠CADareanglessubtendedbythechord
CDtothecircumference.
∴∠CBD=∠CAD=25
o
sincetheangles,subtendedbya
chordofacircletothecircumferenceofthe
samecircle,areequal.
Similarly,∠ACB&∠ADBareanglessubtendedbythechord
ABtothecircumference.
∴∠ACB=∠ADB=35
o
sincetheangles,subtendedbya
chordofacircletothecircumferenceofthe
samecircle,areequal.
Also∠ADC&∠ABCareanglessubtendedbythechord
ABtothecircumference.
∴∠ADC=∠ABC=50
o
sincetheangles,subtendedbya
chordofacircletothecircumferenceofthe
samecircle,areequal.
∴∠BDC=∠ADC+∠ADB=50
o
+35
o
=85
o
.
NowABCDisacyclicquadrilateral.
∴Thesumofitsoppositeangles=180
o
.
So∠BAC+∠BDC=180
o
⟹∠BAC=180
o
−∠BDC=180
o
−85
o
=95
o
.
∴∠DAB=∠BAC−∠CAD=95
o
−25
o
=70
o
.
So
(i)∠CBD=25
o
(ii)∠DAB=70
o
(iii)∠ADB=35
o
Ans−OptionC.
Answer:
35 degree is the answer bro