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sp2606 [1]
3 years ago
11

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 d

irection until she reaches the wall. What is the angle x that her body is making with the wall.​

Mathematics
1 answer:
Georgia [21]3 years ago
7 0

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

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