given ABCD is cyclic quadrilateral whose side AD is the diameter of the circle.if angle CAD=35°. Then find angle CDA and angle ABC
Answers
Answer: In a cyclic quadrilateral, the sum of each pair of opposite angles is 180 degrees.
=> ∠ADC + ∠ABC = 180°
=> 140 ° + ∠ABC = 180°
=> ∠ABC = 40°
AB is diameter
=> ∠ACB = 90° ( angle in semicircle)
in ΔABC
∠BAC + ∠ACB + ∠ABC = 180°
=> ∠BAC + 90° + ∠40° = 180°
=> ∠BAC = 50°
Step-by-step explanation:
Answer:
Correct option is B)
Given:
ABCD is a cyclic quadrilateral with AB as the diameter of the circle.
Also, ∠ADC=140
o
.
We have to find: ∠BAC.
Then,
∠ADC+∠ABC=180
o
....(since the sum of the opposite angles of a quadrilateral is 180
o
).
∴∠ABC=180
o
−140
o
=40
o
.
Also, ∠ACB=90
o
....(since the angle subtended by a diameter at the circumference of the circle, is 90
o
).
∴ In ΔABC we have,
∠ACB=90
o
and ∠ABC=40
o
.
So, ∠CAB=180
o
−(∠ACB+∠ABC)
=180
o
−(90
o
+40
o
)
∴∠BAC=50
o
.