Question

line segment AB and CD intersect at O such that AC paralle. if angle CAB =35° and angle CDB=55°. find angle BOD.

Answer 1

answer is given in the picture uploaded

Answer 2

So, Angle $\angle BOD$ value is $90$°

Step-by-step explanation:

Given;

line segment $AB$ and $CD$ intersect at $O$ such that $AC\parallel BD$ ,$\angle CAB=35degree$ and $\angle CDB=55degree$

∵ $AC\parallel BD$ and $AB$ and $CD$ intersect

∴$\angle CAB=\angle ABD$ and also $\angle BDC=\angle ACD$

∴ $\angle OBD=35$° and $\angle ACO=55$°

From, $\bigtriangleup BDO$,

$\angle BDO+\angle DOB+\angle OBD=180$°

⇒$55+\angle DOB+35=180$

⇒$\angle DOB=180-55-35$

∴$\angle DOB=90$°

∴ Angle $\angle BOD$ value is $90$°