Question

1. find the sum of the measures of exterior angles, one at each vertex, of an octagon.

Answer 1

For #1, C. 1080, For #2, B. 7, For #10, I think its because of the reflexive property (honestly, Google it just to be safe) , And for #11, A Rhombus, Having trouble remembering why but I know its not a rectangle or square.

Answer 2

Answer: First question: b. 360°

Second question : b. 7

Third question: Yes, it is a parallelogram.

Fourth question:  It is a rhombus.

Step-by-step explanation:

1. Since,  The sum of exterior angles in a polygon is always equal to 360 degrees.

And, an octagon is also a polygon.

Therefore the sum of the all exterior angle of an octagon = 360°

2. Since, the sum of the interior angles of a polygon of n sides is (n-2)×180°

But here (n-2)×180°=900

⇒ n-2 = 5 ( After dividing both sides by 180° )

⇒ n = 5 + 2 = 7

Thus,  If the sum of the interior angles of a polygon is 900° then the polygon has 7 sides.

10. Since, In triangles XNY and WNZ,

XN≅NZ (Given)

NY≅NW ( Given)

∠XNY≅∠WNZ ( vertically opposite angles)

Thus, By SAS postulate of congruence,

ΔXNY≅ΔWNZ,

By CPCTC, XY≅WZ

Similarly, Δ XNW≅ Δ YNZ,

By CPCTC, XW≅YZ

Therefore, In quadrilateral XYZW, Opposite sides are equal.

⇒ XYZW is a parallelogram.

11. Let ABCD is a parallelogram,

In which AC is a diagonal.

Also, AB = CD and AD= BC ( By the property of parallelogram)

And, It is given that ∠DAC=∠DCA = 72°

Therefore ADC is an isosceles triangle ( By the property of isosceles triangle)

Thus, AD=DC

Similarly, ABC is an isosceles triangle.

Thus, AB= BC

Thus, AB=BC=CD=DA.

Also, ∠ADC=∠ABC  ( By the property of parallelogram)

Therefore, In ABCD all sides are equal and Opposite angles are equal.

⇒ ABCD is a rhombus. ( The diagram is shown below)