MCQ
Write the correct answer in the following: $ABCD$ is a rhombus such that $\angle\text{ACB}=40^\circ.$ then $\angle\text{ADB}$ is:
- A$40^\circ$
- B$45^\circ$
- ✓$50^\circ$
- D$60^\circ$
✓
Answer
Correct option: C.
$50^\circ$
$ABCD$ is a rhombus such thet $\angle\text{ACB}=40^\circ.$
We know that diagonnals of rhombus bisect each other right angles.
In right $\Delta\text{BOC},$ we have
$\angle\text{OBC}=180^\circ-(\angle\text{BOC}+\angle\text{BCO})$ (angle sum property)
$=180^\circ-(90^\circ+40^\circ)=50^\circ$
$\therefore\ \angle\text{DBC}=\angle\text{OBC}=50^\circ$
Now,
$\angle\text{ADB}=\angle\text{DBC}$ [Alt. int. $\angle\text{s}$ ]
$\therefore\ \angle\text{ADB}=50^\circ[\therefore\angle\text{DBC}=50^\circ]$
Hence, $(c)$ is the correct answer.
We know that diagonnals of rhombus bisect each other right angles.
In right $\Delta\text{BOC},$ we have
$\angle\text{OBC}=180^\circ-(\angle\text{BOC}+\angle\text{BCO})$ (angle sum property)
$=180^\circ-(90^\circ+40^\circ)=50^\circ$
$\therefore\ \angle\text{DBC}=\angle\text{OBC}=50^\circ$
Now,
$\angle\text{ADB}=\angle\text{DBC}$ [Alt. int. $\angle\text{s}$ ]
$\therefore\ \angle\text{ADB}=50^\circ[\therefore\angle\text{DBC}=50^\circ]$
Hence, $(c)$ is the correct answer.
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