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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.​

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 class=

Sagot :

isyllus

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]

View image isyllus
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