In the figure given below- - DAB-100- and - DBC-30- Find- BDC-

Consider ADB and BDC, BD = BD..... (common side) AD = DC..... nbsp; (given) BA = BC..... nbsp; (given) ⇒ ADB ≅ BDC (By SSS criteria) Consider DBC, ⇒∠ DCB ...

You visited us 40 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VIII

Mathematics

Medians of a Triangle and the Drawing Method

In the figure...

Question

In the figure given below, $∠ D A B = 100^{\circ} a n d ∠ D B C = 30^{\circ}$ . Find $∠ B D C$ .

Open in App

Solution

Consider $△ A D B a n d △ B D C,$
BD = BD..... (common side)
AD = DC..... (given)
BA = BC..... (given)
$\Rightarrow △ A D B$ $≅$ $△ B D C$ (By SSS criteria)

Consider $△ D B C,$
$\Rightarrow ∠ D C B = ∠ D A B = 100^{\circ}$ ....(congruent parts of congruent triangle)
$∠ D B C = 30 °$ ....... (given)

$∠ D C B + ∠ C B D + ∠ B D C = 180 °$ ....(Angle sum property of triangle)
$\Rightarrow 100 ° + 30 ° + ∠ B D C = 180 °$
$\Rightarrow 130 ° + ∠ B D C = 180 °$
$\Rightarrow$ $∠ B D C = 180 ° - 130 °$
$\Rightarrow$ $∠ B D C = 50 °$

Suggest Corrections

Similar questions

Q. In the figure given below,

∠ D A B = 100^{\circ} a n d ∠ D B C = 30^{\circ}

. Find

∠ B D C

Q. In the given figure, FDE is the tangent to the circle at point D. If

∠ D A B = 56^{\circ} a n d ∠ D B C = 30^{\circ}

, then the measure of

∠ C D F + ∠ B D C

is equal to

Q. In the given figure, ABCD is a parallelogram in which

∠ D A B

= 75

^{o}

and

∠

DBC = 60

^{o}

then the measure of

∠

BDC is equal to ?

In the given figure, $∠$ DAB = $∠$ CBA and AD = BC. Then which angle is equal to $∠$ ACD?

Q. In the figure,

∠ A B D = 3 ∠ D A B

and

∠ B D C = 96^{o}

, Find

∠ A B D

Join BYJU'S Learning Program

In the figure given below, ∠DAB=100∘and∠DBC=30∘. Find∠BDC.

In the figure given below, $∠ D A B = 100^{\circ} a n d ∠ D B C = 30^{\circ}$ . Find $∠ B D C$ .