Question

ABC is triangle the bisector of exterior angle at angle B and bisector of angle C intersect each other at D prove that angle D =1/2 angle A

Answer 1

Answer:

D=1/2A

Step-by-step explanation:

In ABC,

A+B+C = 180° [Angle sum property] (eq. 1)

In BCD,

B+C+D = 180° [Angle sum property]

(eq. 2)

B+2(angle 1) =180° [Straight line property]

B=180-2(angle 1) (eq. 3)

C=180-2(angle 2) (eq. 4)

Now, substitute the values

A+180-2(angle 1)+180-2(angle 2)=180°

A+180-2(angle 1+ angle 2) =0

Now, In BCD,

B+C+D=180° [Straight line property]

angle 1+ angle 2=180°-D (eq. 5)

Now, substitute the values,

A+180-2(180°-D)=0

A+180-360+2D=0

A-180+2D=0

A+2D=180

D=90-1/2A

Hence proved.....