Question

In the adjacent figure ABC is a triangle in which B = 500 and C= 700 . Sides AB and AC are

produced. If ‘z’ is the measure of the angle between the bisectors of the exterior angles so formed, then

find z.​

Answer 1

Step-by-step explanation:

∘

+x

∘

+50

∘

=180

∘

(Straight angle made on AB at point B)

2x+50

∘

=180

∘

2x=180

∘

−50

∘

=130

∘

x=

2

130

∘

=65

∘

y

∘

+y

∘

+70

∘

=180

∘

(Straight angle made on AC at point C)

2y+70

∘

=180

∘

2y=180

∘

−70

∘

=110

∘

y=

2

110

∘

=55

∘

In △BOC

x+y+z=180

∘

(Angle sum property)

65

∘

+55

∘

+z=180

∘

z=180

∘

−120

∘

=60

∘