Triangles Test

Result

Triangles Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

In triangle ABC, ∠B = ∠C. Bisectors of ∠B and ∠C meet at D. If ∠A = 70°, find ∠BDC.

A
70^o

B
110^o

C
55^o

D
125^o

Solution

By angle sum property of triangle,
70° + ∠B + ∠B = 180° [∵∠B = ∠C]

⇒ 2∠B = 180° – 70°
⇒ 2∠B = 110°
⇒ ∠B = 55°

Also, ∠C = 55°[∵∠B = ∠C]
Now, BD is bisector of ∠B.

Then, ∠1 + ∠2 = 55°
∠2 + ∠2 = 55°[∵ BD is bisector of ∠B]
2 ∠2 = 55°
∠2 = 27.5°

Also, CD is bisector of ∠C.
∠3 + ∠4 = 55°
∠4 + ∠4 = 55°[∠3 = ∠4 as CD is bisector of ∠C.]
2∠4 = 55°
∠4 = 27.5°

Now, in ΔBDC
∠2 + ∠4 + ∠BDC = 180° [Sum of angles of a triangle is 180°.]
27.5° + 27.5° + ∠BDC = 180°

∠BDC = 180° – 55°
∠BDC = 125°