Question

taki has her back to a wall. She starts to walk straight forward. She stops and turns 157° to the right and walks back in this direction until she reaches the wall. What is the angle x that her body is making with the wall.​

Answer 1

`67^\circ`

Explanation:

Given that:

Initially, Taki has her back to a wall and then starts walking straight forward.

Kindly refer to the diagram attached in the answer area.

Initially, Taki was at point A and then moves towards point B.

At point B, Taki turns
`157^\circ` and then starts walking to reach point C at the wall.

To find:

The angle
`x` that her body is making with the wall.

Solution:

As per question statement:

`M\angle B = 157^\circ`

We know that angle on straight line is always
`180^\circ`

i.e.

`M\angle B + m\angle B= 180^\circ\\\Rightarrow 157^\circ + m\angle B= 180^\circ\\\Rightarrow m\angle B = 180-157\\\Rightarrow m\angle B = 23^\circ`

Now, using the angle sum property of a triangle in
`\triangle ABC`:

`m\angle A + m\angle B+ m\angle C = 180^\circ\\\Rightarrow 90+23+x = 180^\circ\\\Rightarrow x = 180 - 90 - 23\\\Rightarrow x = \bold{67^\circ}`

So, our answer is:
`67^\circ`