Mathematics
Answer
In △ ADB,
AD = DB
According to isosceles triangle property,
∠DAB = ∠DBA = 36°
Using exterior angle property,
⇒ ∠DAB + ∠DBA = ∠BDC
⇒ ∠BDC = 36° + 36°
⇒ ∠BDC = 72°
In △ BDC,
DB = CB
According to isosceles triangle property,
∠BDC = ∠BCD = 72°
Sum of all angles in triangle BDC is 180°.
⇒ ∠BDC + ∠BCD + ∠CBD = 180°
⇒ 72° + 72° + ∠CBD = 180°
⇒ 144° + ∠CBD = 180°
⇒ ∠CBD = 180° - 144°
⇒ ∠CBD = 36°
Hence, the value of x = 36°.
Related Questions
If the bisector of an angle of a triangle bisects the opposite side, show that the triangle is isosceles.
The given figure shows a △ABC in which AB = AC and BP = CQ.
Prove that :
(i) △ABQ ≡ △ACP.
(ii) △APQ is isosceles.
In a triangle ABC, AB = AC and ∠A = 36°. If the internal bisector of angle C meets AB at D, prove that AD = BC.
In a triangle ABC, ∠A = x°, ∠B = (3x - 2)° and ∠C = y°. Also, ∠C - ∠B = 9°. Find all the three angles of the △ABC.