MCQ
Write the correct answer in the following: In Fig. if $\angle\text{DAB} = 60^\circ, \angle\text{ABD} = 50^\circ,$ then $\angle\text{ACB}$ is equal to:
- A$60^\circ .$
- B$50^\circ .$
- ✓$70^\circ .$
- D$80^\circ .$
✓
Answer
Correct option: C.
$70^\circ .$
In $\triangle\text{ADB},$ we have
$\angle\text{A}+\angle\text{B}+\angle\text{D}=180^\circ$ [Angle sum property of a triangle]
$\Rightarrow60^\circ+50^\circ+\angle\text{D}=180^\circ$
$\Rightarrow\angle\text{D}=180^\circ-110^\circ=70^\circ$
i.e., $\angle\text{ABD}=70^\circ$
Now, $\angle\text{ACB}=\angle\text{ADB}=70^\circ$
[$\because$ Angles in the same segment of a circle are equal]
Hence, $(c)$ is the correct answer.
$\angle\text{A}+\angle\text{B}+\angle\text{D}=180^\circ$ [Angle sum property of a triangle]
$\Rightarrow60^\circ+50^\circ+\angle\text{D}=180^\circ$
$\Rightarrow\angle\text{D}=180^\circ-110^\circ=70^\circ$
i.e., $\angle\text{ABD}=70^\circ$
Now, $\angle\text{ACB}=\angle\text{ADB}=70^\circ$
[$\because$ Angles in the same segment of a circle are equal]
Hence, $(c)$ is the correct answer.
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