Question

TRY THESE
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Take a regular hexagon Fig 3.10.
1. What is the sum of the measures of its exterior angles x, y, z,p,q,r?
2. Is x=y=z=p=q=r? Why?
3. What is the measure of each?
(1) exterior angle
(ü) interior angle
4. Repeat this activity for the cases of
(1) a regular octagon
(i) a regular 20-gon
Fig 3.10​

Answer 1

Answer:

Step-by-step explanation:

∠p = ∠q = ∠r = ∠x = ∠y = ∠z =  180 ° -  ∠a

Interior angle = 120°

Exterior angle = 60°

Step-by-step explanation:

∠a + ∠p = 180 ° ( straight line)

Similarly

∠a + ∠q = 180 °

∠a + ∠r = 180 °

∠a + ∠x = 180 °

∠a + ∠y = 180 °

∠a + ∠z = 180 °

∠p = ∠q = ∠r = ∠x = ∠y = ∠z =  180 ° -  ∠a

Adding all

6∠a + 6∠p = 1080°

Interior Angle

The sum of the measures of the interior angles of a polygon with n sides is (n – 2)180° = (6-2)*180° = 720°

one interior angle = 720/6 = 120°

Exterior Angle =  180°  - 120° = 60°