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Pachacha [2.7K]
2 years ago
6

Someone please help me.

Mathematics
1 answer:
adoni [48]2 years ago
6 0
<h3>Answer:  16 feet</h3>

Work Shown:

L = d+9 = length along the horizontal

W = 10 feet = width along the vertical

P = 2(L+W) = perimeter of rectangle = 70 feet

70 = 2(d+9+10)

70/2 = d+19

35 = d+19

d+19 = 35

d = 35-19

d = 16

The deep end is 16 feet wide

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In the figure below, a shaded polygon, which has equal sides and equal angles, is partially covered with a sheet of blank paper.
Zepler [3.9K]

Answer:

The polygon has 9 sides ⇒ D

Step-by-step explanation:

This is a tricky question

∵ The shaded figure is a quadrilateral

∴ The sum of the measures of its angles is 360

∵ Its angles are <u>x, y, and two vertices of the polygon</u>

∵ All angles of the polygon are equal in mesures

∴ x + y + m of 2 vertices = 360°

∵ x + y = 80

→ Substitute the value of x + y above by 80

∴ 80 + m of 2 vertices = 360

→ Subtract 80 from both sides

∴ m of 2 vertices = 280

→ Divide the two sides by 2

∴ m of 1 vertex = 140°

∴ The measure of each angle of the polygon is 140°

<em>The sum of the measures of the </em><em>interior angle and the exterior angle</em><em> at any vertex of the polygon is </em><em>180°</em>

∵ m of interior ∠ + m of exterior ∠ = 180° ⇒ at any vertex

∴ 140 + m of exterior ∠ = 180°

→ Subtract 140 from both sides

∴ m of exterior ∠ = 40°

∴ The measure of each exterior angle is 40°

<em>The </em><em>sum </em><em>of the measures of the </em><em>exterior angles</em><em> of any polygon is </em><em>360°</em>

∵ The measure of each exterior angle of the given polygon is 40°

∴ The number of the angles of the polygon = 360 ÷ 40 = 9

∵ The number of the angles of the polygon = the number of its sides

∴ The polygon has 9 sides

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