Question

In triangle abc, the bisector of angle b and angle c meet at point o within the triangle. if angle boc is equal to 148 degree, then the measure of angle a is

Answer 1

Answer:

116°

Explanation:

in triangle boc

<obc =1/2 b

<ocb =1/2 c

<boc = 148°

1/2 b +1/2 c +148°= 180°

1/2 b + c = 180 °-148°

1/2 b+c = 32

b+c = 32 ×2

= 64

a + b +c = 180°

a + 64 =180

a =180 -64

a = 116

Answer 2

Given :

The measure of ∠ boc = 148°

where , o is point where bisector of angle b and angle c meet .

To find :

The measure of angle a .

Solution :

The measure of ∠ boc = 148°

In a triangle , sum of all angles are equal to 180° .

In Δ boc ,

[ ( ∠ b + ∠ c ) / 2 ] + ∠ boc = 180°

→  [ ( ∠ b + ∠ c ) / 2 ] +  148° = 180°

→ ( ∠ b + ∠ c ) / 2 = 32°

→  ∠ b + ∠ c = 64°

then , in Δabc ,

∠ a + ∠ b + ∠ c = 180°

→ ∠a + 64° = 180°

→ ∠a = 116°

The measure of angle a = 116°