What is the sum of the measures of the interior angles of a pentagon and 10-gon (decagon)?
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the sum of the measures of the interior angles of a pentagon is 540 degrees and that of a decagon is 1440 degrees

Step-by-step explanation:

The formula for finding the sum of the measure of the interior angles in a regular polygon is expressed as (n - 2) × 180.

A Pentagon has 5 sides. This means that the sum of the angles in a heptagon is

180(5 - 2) = 180 × 3 = 540 degrees

A Decagon has 10 sides. This means that the sum of the angles in a heptagon is

180(10 - 2) = 180 × 8 = 1440 degrees

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step-by-step explanation:

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°