Question

ABC is a right triangle when angle ABC is 90° and D is the mid point of AC. If AB=1/2 AC. Find angle BDC.

PLEASE ANSWER FAST!!!!!​

Answer 1

Answer:

∠BDC = 90°

Step-by-step explanation:

We know that ABC is a right triangle.

∠B = 9

AB = 1/2 AC (given)

 =) 2AB = AC...(i)

Here,

   AD + DC = AC

=) 2AD = AC...(ii)

From equation (i) and (ii)

AD = AB...(iii)

Now,

∠DBC =1/2* 90° = 45°...(iv)

In triangle ABC,

∠BAC + ∠BCA = 90°

⇒ ∠BCA + ∠BCA = 90°

⇒ 2∠BCA = 90°

⇒ ∠BCA = 45°...(v)

In triangle BCD,

∠DBC = 45°

∠BCD = 45°

So, 45° + 45° + ∠BDC = 180° (angle sum property)

  ⇒ 90° + ∠BDC = 180°

 ⇒ ∠BDC = 180° - 90°

 ⇒ ∠BDC = 90°