The question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer:
Assertion (A) | Reason (R) |
In the given figure, ∠ABC = 70° and ∠ACB = 30°. Then, ∠BDC = 70°.
| In the given figure, ∠AOC = 130°, then ∠ABC = 115°.
|
Assertion (A) :
Here, in ΔABC
By angle sum property
∠ABC + ∠BCA + ∠CAB = 180°
70° + 30° + ∠CAB = 180°
∠CAB = 180° – 70° – 30° = 80°
∠CAB = ∠BDC = 80° (angles in same segment)
But given that ∠BDC = 70°
∴ Assertion(A) is wrong.
Reason (R) :
∠ ADC = 
∠ AOC = 
× 130° = 65°
∠ ABC + ∠ ADC = 180°
∠ ABC + 65° = 180°
∠ABC = 180° – 65° = 115°
Reason (R) is true
Assertion (A) :
∠ABC + ∠BCA + ∠BAC = 180°
70° + 30° + ∠BAC = 180°
∠BAC = 180° – 70° – 30°
∠ BAC = 80°
∴ ∠BDC = ∠BAC = 80° (angles in the same segment)
This is false.
Thus, Assertion (A) is false and Reason (R) is true.
Hence, correct choice is D