Question

In the adjacent figure, ABC is a triangle in which
B = 50° and C=70°. 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

$\sf{\purple{\large{\boxed{z = 60{\degree}}}}}$

$\text{\underline{\underline{\huge{\red{Solution}}}}}$

Here,

ABC is a triangle in which ∠B = 50° and ∠C = 70° .sides AB and AC are produced two rays,

Such that, z' is the measure of the angle between the bisectors of the exterior angles so formed,

Now, AB is a straight line,

Thus, by the diagram,

x° + x° + 50° = 180°,

2x° + 50° = 180°

2x° = 130°

x = 65,

Similarly, again by the diagram,

y° + y° + 70° = 180°,

2y° + 70° = 180°

2y° = 110°

y = 55,

Now, OBC is a triangle,

⇒ ∠BOC + ∠OBC + ∠BCO = 180°,

⇒ z + x + y = 180

⇒ z + 65 + 55 = 180

⇒ z = 180 - 120 = 60

$\sf{\green{Hence,\:z = 60{\degree}}}$

Hope this helps!!