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3 years ago

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

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Plug in the value of r

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

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Area of the parallelogram = $bh$

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Plug in the value of b and h

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f. Triangle = 21.6 sq. ft

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