Which of the following types of polygons do not exist?
(i) parallelogram with right angles
(ii) isosceles trapezoid with all obtuse angles
(iii) quadrilateral with all acute angles
(i) and (ii) only
(i) and (iii) only
(ii) and (iii) only
None of the other choices

5. Consider the following diagram. Which statement, if either, is true?
(i) m∠4 + m∠5 + m∠6 = 180°
(ii) m∠7 + m∠8 + m∠9 = 360°
A) (i) only
B) (ii) only
C) Both (i) and (ii)
D) Neither (i) nor (ii)

Parallelogram with right angles is called a rectangle. Pretty sure they exist.
Trapezoids have four sides, two of which are parallel. Like all quadrilaterals, they have a total of 360 degrees of interior angle. It is hard to get four obtuse angles to total to only 360.
Similarly, a quadrilateral with four acute angles will have a hard time summing to 360 degrees.
Seems to me that (ii) and (iii) are conditions that are hard to meet.