Question

In the given figure, ABCD is a
parallelogram, in which DAB = 75 and
DBC = 60° ,then find ABD​

Answer 1

$\large\underline\bold{Question:-}$

In the given figure, ABCD is a

parallelogram, in which DAB = 75 and

DBC = 60° ,then find ∠ABD.

$\large\underline\bold{Answer:-}$

$\small\underline\bold{Given:-}$

$\sf\ ABCD\:is\:a\: Parallelogram,\: in\: which\: ∠DAB= 75°$

$\sf\ and\: ∠DBC =60°$

$\small\underline\bold{To\:Find:-}$

$\sf\ ∠ABD$

$\small\underline\bold{Required\: Solution:-}$

$\sf\ In\: Parallelogram$

⟹$\sf\ DAB+ABC = 180°$

$\sf\ So,$

⟹$\sf\ ∠ABC= 180°-75°=105°$

⟹$\sf\ ∠ABD = ∠ABC - ∠DBC$

⟹$\sf\ =105°-60°=45°$

$\sf\ In\:triangle \:∠ABD$

⟹$\sf\ ∠ADB=180-∠DAB-∠ADB=60°$

$\sf\ As\:AB\:and\:CD\: parallel$

$\sf\ ∠CDB=∠ABD$

$\small\underline\bold\purple{Hence,\:∠ABD=45°}$

Answer 2

∠A + ∠B = 180°

⇒ 70° + ∠B = 180°

⇒ ∠B = 110°

⇒ ∠ABD + ∠DBC = 110°

⇒ ∠ABD + 65° = 110°

⇒ ∠ABD = 45°

Now, ∠CDB = ∠ABD = 45