Question

In the quadrilateral ABCD, $\angle$ CDA and $\angle$ DAB are right angles and $\angle$CBA is the half of $\angle$ DCB. Find the value of $\angle$CBA.

• A. 60°
• B. 70°
• C. 80°
• D. 90°

Answer 1

The correct option is D 90°

By angle sum property, sum of all the interior angles of a quadrilateral add up to 360°.

Given, $\angle$ CDA and $\angle$ DAB are right angles and $\angle$CBA is the half of $\angle$ DCB.


From the figure,
$\angle$ CDA = $\angle$ DAB = 90° ...(i)
$\angle$ DAC = $x$, $\angle$ABD = $\frac{x}{2}$ ...(ii)

By angle sum property,
$\angle$ABC + $\angle$ BCD + $\angle$ BAD + $\angle$ABD = 360°.
$\to$ $90°+90°+x+\frac{x}{2}=360°$
$\to$ $180°+\frac{3x}{2}=360°$
$\to$ $360°+3x=720°$
​​​​​​​$\to$ $3x=720°-360°=360°$
​​​​​​​$\to$ $x=\frac{360°}{3}=120°$
​​​​​​​
Hence, from(i) and (ii),
$\angle$ DAC = $x$ = 120°
$\angle$ABD = $\frac{x}{2}=\frac{120°}{2}=60°$