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3 years ago

Work out the angle of x please answer ASAP!!

Mathematics

1 answer:

geniusboy [140]3 years ago

6 0

Given:

The figure of a pentagon.

To find:

The value of the x.

Solution:

We know that, the sum of all interior angles of a pentagon is 540 degrees. So,

$(5x-25)+(6x+25)+(6x-3)+(9x)+(7x+15)=540$

$(5x+6x+6x+9x+7x)+(-25+25-3+15)=540$

$33x+12=540$

Subtract both sides by 12.

$33x+12-12=540-12$

$33x=528$

Divide both sides by 33.

$x=\dfrac{528}{33}$

$x=16$

Therefore, the value of the x is 16.

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Theorem: The segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length. A two-c

natali 33 [55]

Answer: By the slope formula.

Step-by-step explanation:

Given: ABC is a triangle (shown below),

In which A≡(6,8), B≡(2,2) and C≡(8,4)

And, D and E are the mid points of the line segments AB and BC respectively.

Prove: DE║AC and DE = AC/2

Proof:

Since, And, D and E are the mid points of the line segments AB and BC respectively.

Therefore, By mid point theorem,

coordinate of D are $(\frac{2+6}{2} , \frac{2+8}{2} ) = (\frac{8}{2} , \frac{10}{2} )= (4,5)$

Coordinate of E are $(\frac{2+8}{2} , \frac{2+4}{2} ) = (\frac{10}{2} , \frac{6}{2} )= (5,3)$

By the distance formula,

$DE=\sqrt{(5-4)^2+(3-5)^2}=\sqrt{5}$

$AC=\sqrt{(8-6)^2+(4-8)^2}=2\sqrt{5}$

By the slope formula,

Slope of AC = $\frac{4-8}{8-6} = \frac{-4}{2} = -2$

Slope of DE = $\frac{3-5}{5-4} = \frac{-2}{1} = -2$

Statement Reason

1. The coordinate of D are (4,5) and 1. By the midpoint formula

the coordinate of E are (5,3)

2. The length of DE = √5 2. By the Distance formula

The length AC = 2√5 ⇒ Segment DE

is half the length of segment AC

3. The slope of DE = -2 and the 3. By the slope formula

slope of AC = -2

4. DE║AC 4. Slopes of parallel lines are equal

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