Question

1. consider the polygon shown. use the given information to answer the following questions. determine the value of x. determine the value of y.

Explanation:

Step1: Recall sum of exterior angles of polygon

The sum of the exterior angles of any polygon is 360°.

Step2: Set up equation

We have the exterior - angle measures 67°, 75°, x°, and y°. So, 67 + 75+x + y=360.

Step3: Simplify the left - hand side

67+75 = 142, so the equation becomes 142+x + y=360.

Step4: Assume the polygon is a quadrilateral (since 4 exterior angles are shown) and if it is a regular - like situation (no other information given about relationships), we can't directly solve for x and y separately without more information. But if we assume the polygon is a convex quadrilateral and we know that exterior angles are supplementary to interior angles. Let's assume the polygon is a non - special quadrilateral. We know that for a polygon, the sum of exterior angles is 360°.

If we assume the polygon is a convex quadrilateral and we have no other angle - related information, we can assume the sum of the two unknown exterior angles x + y=360-(67 + 75)=360 - 142 = 218.
If we assume the polygon is symmetric or has some equal - angle properties (again, without more information, this is an assumption), and if we assume the two unknown angles are equal (a very basic assumption in the absence of other data), then x=y.
So x=y = 109.

Answer:

x = 109, y = 109