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3 years ago

Find the interior angle sum of this polygon. Can someone help????

Mathematics

1 answer:

Savatey [412]3 years ago

6 0

<h3>Answer: 1440 degrees</h3>

===================================================

Explanation:

See the diagram below. It shows there are 10 sides, so n = 10.

We'll plug this value of n into the formula below to find the sum of all ten interior angles

S = sum of interior angles

S = 180(n-2)

S = 180(10-2)

S = 180(8)

S = 1440 degrees

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A different approach:

Let's assume this polygon is a regular polygon. This means each angle is congruent to one another.

We have n = 10 sides, so each exterior angle is E = 360/n = 360/10 = 36 degrees.

Each interior angle adjacent to this 36 degree exterior angle is

180-E = 180-36 = 144 degrees

Since we have 10 equal angles of 144 degrees each, so overall the interior angles add to 10*144 = 1440 degrees

Side note: if this polygon is not a regular polygon, then this section does not apply. You would use the first method instead.

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2 years ago

Find the slope of the line that is (a) parallel and (b) perpendicular to the line through the pair of points.

ddd [48]

Answer:

a) The slope of the line is parallel to the another line m=4

b) The slope of the line is perpendicular to the another line m= $\frac{-1}{4}$

Step-by-step explanation:

Step1:-

Slope of a line :-

If θ is the inclination of a line 'l' then tanθ is called the slope or gradient of the line 'l'.The slope of a line is denoted by m=tanθ

The slope of a line given two points m= $\frac{y_{2}-y_{1} }{x_{2} -x_{1} }$

Parallel lines:-

Two non-vertical lines are parallel if and only if their slopes are parallel

Perpendicular lines:-

Two non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.

$m_{2} = \frac{-1}{m_{1} } \\$

Step 2:-

a)The slope of a line when given two points (-1,-4) and (0,0)

$m = \frac{0-(-4)}{0-(-1)} =4$

Two non-vertical lines are parallel if and only if their slopes are parallel

$m_{1} = m_{2}$

Therefore the slope of the line that is parallel to the another line

$m_{1} =m_{2} =4$

Step 3:-

b) Two non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.

$m_{2} = \frac{-1}{m_{1} } \\$

$m_{2} =\frac{-1}{4}$

Therefore the slope of the line is perpendicular to the another line is

$m=\frac{-1}{4}$

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masha68 [24]

Answer:

135

Step-by-step explanation:

Given:

$x = 5$

To determine a numerical value for the expression, simply substitute the value of "x" into the expression and simplify the expression, if necessary, to determine a specific number for the expression provided.

$\implies 5x^{2} + 2x$

$\implies 5(5)^{2} + 2(5) \longrightarrow \longrightarrow \longrightarrow (x = 5)$

$\implies 5(5)(5) + 2(5)$

$\implies 125 + 10$

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Therefore, the value of the expression $5x^{2} + 2x$ when x = 5 is 135.

Learn more about this topic: brainly.com/question/27675691

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