Find the value of x. Show your work.

Mathematics

1 answer:

r-ruslan [8.4K]4 years ago

5 0

Exterior angle sum of an polygon (shape) is 360 degrees (this is a property)

x + 98 + 41 + 76 + 86 = 360

Therefore x = 59

Please double check the equation I have written. Your picture is a bit blurry therefore I can really tell what number is 6 and 8. Sorry

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In the given figure find the area of the shaded region if AC = 24 CM AB = 7cm and O is the centre

wariber [46]

See the attached figure to better understand the problem

we know that

The inscribed angle in a circle measures half of the arc it comprises.

in this problem
the inscribed angle= ∠ACB
and the arc it comprises measures 180°
then
the ∠ACB=180°/2-------> ∠ACB=90°

applying the Pythagorean theorem
AC²+CB²=AB²-------> AB²=24²+7²-------> AB²=625------> AB=25 cm

the diameter of circle is AB
radius=25/2--------> r=12.5 cm

[the area of a half circle]=pi*r²/2------> pi*12.5²/2--------> 245.44 cm²

[area of triangle ABC]=AC*CB/2--------> 24*7/2-------> 84 cm²

[the area of the shaded region]=[the area of a half circle]-[area of triangle ABC]

[the area of the shaded region]=245.44-84-------> 161.44 cm²

the answer is
the area of the shaded region is 161.44 cm²