Find the number of diagonals of a regular polygon whose interior angle measures 144 degrees?

2 answers:

7 0

Diagonals are = n - 2

Interior = 144

Exterior angle = 180 - 144 = 36

Formula for exterior of a regular polygon given the number of sides:

= 360/n

36 = 360/n

n = 360/36 = 10

n = 10

Number of diagonals = n - 2 = 10 - 2 = 8

8 diagonals.

gtnhenbr [62]3 years ago

6 0

For this specific problem, the number of diagonals of a regular polygon whose interior angle measures 144 degrees is 35. I am hoping that this answer has satisfied your query about and it will be able to help you, thank you and have a nice day.

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Find the angle made by the x axis and the terminal side resulting from connecting the origin to (5,7), rounded to the nearest in

prohojiy [21]

<h2>Answer:</h2>

55°

<h2> Step-by-step explanation:</h2>

To solve this, follow these steps:

i. <em>Make a sketch of the problem</em>.

The sketch has been attached to this response.

ii. <em>Label the sketch properly</em>

As shown in the sketch, θ is the angle between the x-axis and the terminal side resulting from connecting the origin to (5,7).

iii. <em>Solve using the tangent trigonometric ratio</em>

With the proper sketch and labelling, a right triangle is formed with the adjacent and opposite sides to the angle being 5 units and 7 units respectively.

Using the tangent formula,

tan θ = opposite / adjacent

tan θ = 7 / 5

θ = tan⁻¹ (7/5)

θ = tan⁻¹ (1.4)

θ = 54.46

θ = 55° to the nearest integer.

Therefore, the angle made by the x axis and the terminal side resulting from connecting the origin to (5,7), rounded to the nearest integer is 55°