The interior angles of a hexegon are in the ratio 3:3:4:5:6:7. Find; (a) The size of the smallest angle. (b) The size of the largest angle

a) 77.13

b) 179.97

Step-by-step explanation:

3x + 3x + 4x + 5x + 6x + 7x = (6 - 2) × 180

28x = 720

x = 720/28

x ≅ 25.71

3 × 25.71 = 77.13 = smallest angle

7 × 25.71 = 179.97 = largest angle

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!

80° is the measure of gh

step-by-step explanation:

circle f is congruent to circle j

we have two circle with center f and j.

both circles are congruent. the radius of the circle would be equal.

see the attachment for the circle.

we are given ∠efd ≅ ∠gjh

therefore, arc (ed) = arc (gh)     (∴ circle f is congruent to circle j)

but ∠dfe=80°=arc (ed)

therefore, arc (gh) = 80°

thus, 80° is the measure of gh