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kkurt [141]
3 years ago
11

The measures of interior angle of a convex pentagon are in ratio 1:2:3:4:5. Find the measures of each angle

Mathematics
1 answer:
vovangra [49]3 years ago
3 0

Answer:

The angles have measurements 36, 72, 108, 144, and 180.

Step-by-step explanation:

Pentagon has 5 sides and 5 angles.

The amount of triangles formed by choosing one vertex and drawing from that vertex to every nonadjacent vertex is 3.

3(180)=540 which is the sum of the angles in a pentagon.

So since the ratio is 1:2:3:4:5, that means the angles are 1x,2x,3x,4x, and 5x.

We have the equation 1x+2x+3x+4x+5x=540 to solve.

15x=540

Divide 15 on both sides:

x=540/15

x=36

1x=36

2x=72

3x=108

4x=144

5x=180

The angles have measurements 36, 72, 108, 144, and 180.

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Let X the random variable of interest, on this case we now that:  

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The probability mass function for the Binomial distribution is given as:  

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Applying the formula for each identified shape that are given, the correct areas to each shape are:

a. <em>Square </em>= 134.6 sq. yd

b. <em>Circle </em>= 452.2 sq. cm

c. <em>Parallelogram </em>= 40.6 sq. cm

d. <em>Rectangle </em>= 43.2 sq. ft

e. <em>Trapezium </em>= 25.7 sq. m

f. <em>Triangle</em> = 21.6 sq. ft

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Area of the square = s^2

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s = 11.6 yd

Plug in the value of s

Area of the square = 11.6^2 = 134.6 $ yd^2

b. The shape given is a circle.

Area of the circle = \pi r^2

  • Where,

r = 12 cm

  • Plug in the value of r

Area of the square = \pi \times 12^2 = 452.2 $ cm^2

c. The shape given is a parallelogram.

Area of the parallelogram = bh

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b = 7 cm

h = 5.8 cm

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Area of the parallelogram = 7 \times 5.8 = 40.6 $ cm^2

d. The shape given is a rectangle.

Area of the rectangle = l \times w

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l = 8.3 ft

w = 5.2 ft

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e. The shape given is a trapezium.

Area of the trapezium = \frac{1}{2} (a + b)  \times h

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a = 2.8 m

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f. The shape given is a triangle. <em>(See attachment for the shape).</em>

Area of the triangle = \frac{1}{2}  \times b  \times h

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b = 9 ft

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  • Plug in the value of b, and h

Area of the triangle = \frac{1}{2} \times 9 \times 4.8 = 21.6 $ ft^2

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e. <em>Trapezium </em>= 25.7 sq. m

f. <em>Triangle</em> = 21.6 sq. ft

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brainly.com/question/22560863

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