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

Answer:

$67^\circ$

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 $157^\circ$ 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: $67^\circ$