Find the number of sides of a regular polygon whose each exterior angle has a measure of 72°.

Step-by-step explanation:

The sum of the exterior angles of a polygon = 360°

The formula for calculating the size of an exterior angle is:

exterior angle of the polygon = 360 ÷ n

(where n is the number of sides)

Therefore,                            72 = 360 ÷ n

Multiply both sides by n:   72n = 360

Divide both sides by 72:         n = 5

Therefore, a polygon whose exterior angle has a measure of 72° has 5 sides.

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m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°