= You need to notice that the measure of angle `hat(ADB)`  may be evaluated in triangle `Delta ADB`  such that:

`hat(ADB) = 180^o - (hat A+ hat(ABD))`

You need to notice that the angle `hat(BDC)`  may be evaluated in triangle `Delta BDC`  such that:

`hat(BDC) = 180^o - (hatC+ hat(CBD))`

Adding the angles `hat(ADB)`  and `hat(BDC)`  yields:

`hat(ADB) + hat(BDC) = 360^o - hat A - hat C - (hat(ABD) + hat(CBD))`

`hat(ADB) = 360^o - hat A - hat C - hat B - hat(BDC)`

Hence, evaluting the measure of angle `hat(ADB)` , based on the drawing provided by the problem, yields `hat(ADB) = 360^o - hat A - hat C - hat B - hat(BDC` ), hence, the given answer is false.