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A.\[{45^ \circ }\]

B.\[{36^ \circ }\]

C.\[{144^ \circ }\]

D.\[{44^ \circ }\]

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We will get measure of each interior angle. Then using the formula: exterior angle \[ = \]\[{180^ \circ } - \] interior angle we will get the required answer.

We have given the aperture of a camera is formed by 10 blades overlap to form a regular decagon.

As we know the sum of interior angles of \[n - \]sided polygon \[ = \] \[\left( {n - 2} \right) \times 180\].

Here, we have decagon

So, \[n = 10\]

Hence, sum of interior angles of decagon \[ = \left( {10 - 2} \right) \times {180^ \circ }\] \[ = 8 \times {180^ \circ }\]

\[ \Rightarrow \]Sum of angles of interior angles of decagon\[ = {1440^ \circ }\]

Now, using the formula for calculating each interior angle of a polygon \[ = \] \[\dfrac{{\left( {n - 2} \right)180}}{n};\] where n is the number of sides of polygon.

Here, \[n = 10\] so we get,

Each interior angle of a decagon \[ = \] \[\dfrac{{\left( {10 - 2} \right)180}}{{10}}\]

\[ \Rightarrow \dfrac{{8 \times 180}}{{10}}\] \[ = 8 \times 18\]

\[ \Rightarrow {144^ \circ }\]

Hence, we get each interior angle of a decagon is of\[{144^ \circ }\].

So, from the figure we can say that \[\angle JAB = {144^ \circ }\]

Now,

Use the fact that, exterior angle \[ = \]\[{180^ \circ } - \] interior angle

Here, we have\[\angle JAB = {144^ \circ }\]

Therefore, exterior angle of a decagon \[ = {180^ \circ } - {144^ \circ }\]

\[ = {36^ \circ }\]

From the figure we can say that \[\angle BAX\]is an exterior angle.

\[\therefore \angle BAX = {36^ \circ }\]

Thus, the measure of \[\angle BAX\] is \[{36^ \circ }\]

Exterior angle of a polygon is an angle at a vertex of the polygon, outside the polygon, formed by one side and the extension of an adjacent side.

The sum of exterior angles of a polygon must be \[{360^ \circ }\].