Question

Find the measure of x, y and z without actually measuring them.

Answer 1

160=y. vertically opposite
160+z =180. straight line
z=20
z=x
x=20

Answer 2

Heya!!!

Here is your answer :-

What are vertically opposite angles ?
- Vertically opposite angles are those angles which are formed by two intersecting lines. They are equal.

V.O.A => Vertically opposite angles.

Main Solution : -

y = 160° ( Vertically opposite angles )

x = z ( Vertically opposite angles )

We know that sum of angles all around a point is equal to a complete angle i.e two straight line angles.

Therefore,

x + y + z + 160° = 360°

Substituting the values of angles , we get : -

x + 160° + x + 160 ° = 360 °

Using transposition to solve for x ,

2x + 320° = 360°

2x = 40°

x = 20°

Therefore,

z = x = 20°

So, the measures of x , y and z are :-

x = 20°

y = 160°

z = 20°

Hope it helps you.