Question

if one of the angles of a triangular is 130, find the angle between the bisectors of other two angles

Answer 1

Jen’s DVDhendnnebebebehebbebebr

Answer 2

As shown in the figure:

Angle A=130(given)

TO FIND : Angle DPE = Angle CPB =?

Let angle B be 2x

So, angle C = 180 - (130 +2x) = 50–2x

So angle DCB =(50–2X)/2

Now, angle CDA = 2x + (50–2x)/2 ( as exterior angle = the sum of 2 opposite interior angles)

=> angle CDA = (2x +50)/2 = x+ 25 ……..(1)

Now,in triangle AEB, angle AEB =180 - (130+x) = 50 -x ………….(2)

So, in quadrilateral ADPE,

angle DPE = 360 -(130 + x+25 + 50-x)

=> angle DPE = 360- 205

=> angle DPE = 155°