Write the correct answer in the following: ABCD is a rhombus such… - Vidyadip

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
40º
B
45º
C
50º
D
60º

✓

Answer

50º
Solution:
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.

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