Question

A square and a regular heptagon are coplanar and share a common side $\overline{AD}$, as shown. What is the degree measure of exterior angle $BAC$? Express your answer as a common fraction.

Answer 1

Answer:

$\angle BAC = 141\frac{3}{7} ^{\circ}$

Step-by-step explanation:

The interior angle of a regular heptagon = = 900/7° = 128.57°

Therefore, angle DAB = 128.57°

The interior angle of the square = 90°

Therefore, angle DAC = 90°

Therefore, we have

angle DAB+ angle DAC + angle BAC = 360° (sum of angles at a point (A))

Angle BAC = 360° - angle DAB - angle DAC =  360° - 900/7° - 90° = 990/7°

Angle BAC = 141.43°

Expressing 141.43° as a common fraction gives;

$141.43 ^{\circ}= \dfrac{990}{7} ^{\circ}=141\frac{3}{7} ^{\circ}$

$\angle BAC = 141\frac{3}{7} ^{\circ}$

Answer 2

 The degree measure of exterior angle BAC is $141\frac{3}{7}^\circ$

Given, A square and a regular heptagon are coplanar as shown in below figure attached.

We have find the exterior angle of BAC.

We know that, The formula that gives the interior angle measure for a regular polygon with any number of sides is,

$\frac{180(n-2)}{n}$  where n is the number of sides.  

Since the heptagon has 7 no. of sides.

So regular heptagon's interior angle measures,

$\frac{180(7-2)}{7}=128\frac{4}{7}$

Hence $\angle A$ will be$128\frac{4}{7}$ degrees.

We know that a square's interior angle is 90 degrees and a heptagon's interior angle is  128.57 degrees. We will subtract those from 360 degrees to find angle BAC.

$\angle BAC = 360 - (\angle A + 90)$

$\angle BAC = 360 - (128\frac{4}{7} + 90)\\\angle BAC=141\frac{3}{7} ^\circ$

Hence the degree measure of exterior angle BAC is $141\frac{3}{7}^\circ$.

For more details on Exterior angle follow the link:

https://brainly.com/question/2125016