Question

ABCD is a parallelogram in which $\angle$DCB and $\angle$ABC are in ratio 2:7. Find the sum of $\angle$ABD and $\angle$ADB.

Answer 1

$\angle$DCB + $\angle$ABC = 180°
[Adjacent angles of a parallelogram are supplementary]

2t + 7t = 180°
because $\angle$DCB and $\angle$ABC are in ratio 2:7]
t = 20°
$\angle$DCB = 2t = 2 × 20° = 40°
and $\angle$ABC = 7t = 7 × 20 ° = 140°

Now, $\angle$DAB=$\angle$DCB=40°
(Opposite angles of a parallelogram are equal)

$\angle$DAB + $\angle$ADB + $\angle$ABD = 180°
(Sum of the angles of a triangle)

40° + $\angle$ADB + $\angle$ABD = 180°
$\angle$ADB + $\angle$ABD = 140°