Question

6. In Diagram 1, NPQRSTUV is a regular octagon. NVW and STW are straight lines.

Answer 1

Answer:

  A.  37.5°

Step-by-step explanation:

∠SPT can be considered an inscribed angle in the circumcircle. In that circle, arc ST would have a measure of 360°/8 = 45°. Angle y° is half that measure, so is 22.5°.

The external angles of a regular octagon are 360°/8 = 45°, so that is the measure of angles UTW and UVW. It is also the amount by which reflex angle TUV exceeds 180°.

The sum of the interior angles of quadrilateral TUVW is ...

  45° +225° +45° +3x° = 360°

Then 3x° = 45° and x° = 15°.

Then the sum of interest is ...

  x° + y° = 15° + 22.5° = 37.5°