State whether the following statements are true or false, and explain your reasoning. a) A square is a rectangle.
b) A polygon with 21 sides has 432 possible diagonals.
c) All three angles in an Isosceles triangle are equal.
d) The measures of the exterior angles of a nonagon, a nine-sided figure, have a sum of 360°.

Step-by-step explanation:

a) A square is a rectangle.   True

Reason: Property of Rectangle: (i) Opposite sides are equal and parallel. (ii) Each angle is 90 (iii) Diagonals are equal and bisect each other.

A square hold all these properties. A square is  a rectangle.

b) A polygon with 21 sides has 432 possible diagonals. False

Reason: Number of diagonals of a polygon =

n --> number of sides of a polygon.

= = 189 diagonals

c) All three angles in an Isosceles triangle are equal. False

Reason: In an isosceles triangle, two angles are equal.

If three angles are equal, then that is an equilateral triangle.

d) The measures of the exterior angles of a nonagon, a nine-sided figure, have a sum of 360°. True.

Reason: The sum of measures of the exterior angles  of any polygon is 360

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this