Answer:
[tex]67^\circ[/tex]
Step-by-step 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 [tex]157^\circ[/tex] and then starts walking to reach point C at the wall.
To find:
The angle [tex]x[/tex] that her body is making with the wall.
Solution:
As per question statement:
[tex]M\angle B = 157^\circ[/tex]
We know that angle on straight line is always [tex]180^\circ[/tex]
i.e.
[tex]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[/tex]
Now, using the angle sum property of a triangle in [tex]\triangle ABC[/tex]:
[tex]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}[/tex]
So, our answer is: [tex]67^\circ[/tex]
