Question

4:5. Find the acute angles of
11. When the three sides of a triangle are produced as
shown:
X
2
3
С
B
2
Show that x + y + z = 360°.
(Hint x= Z1 + Z2, Zz = Z1 + Z3.
Zy= 22 + 23. Adding their both sides we get the
result).​

Answer 1

Answer:

z

1

−z

3

)

=

2

1

−

2

i

3

⟶(1)

Apply argument on both sided

⇒Arg

(z

2

−z

3

)

(z

1

−z

3

)

=(

2

1

−

2

i

3

)Arg

⇒Arg

(z

2

−z

3

)

(z

1

−z

3

)

=

3

π

Angle between z

i

3

2

&z

2

−z

3

is 60°

By similarly substract 1 on both sides of (1)

⇒

z

2

−z

3

z

1

−z

3

−1=

2

−1

−

2

i

3

⇒

z

2

−z

3

z

1

−z

3

−z

2

+z

3

−1=

2

−1

−

2

i

3

Apply argument on both sides we get

⇒Arg

(z

2

−z

3

)

(z

1

−z

3

)

=

3

π

Angle between z

1

z

2

&z

3

+z

2

is 60° Obviously other angle is 60° equilateral triangle.

Hence, the answer is equilateral