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➷ Use this formula to work out the sum of interior angles:
(n - 2) x 180
n is the number of sides
(5 - 2) x 180 = 540
Now we know the sum of interior angles is 540
(5x - 12) + (2x + 100) + (4x + 16) + (6x + 15) + (3x + 41) = 540
Simplify:
20x + 160 = 540
Subtract 160 from both sides:
20x = 380
Divide both sides by 20:
x = 19
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A convex pentagon has an interior angle with measures of x = 19.
How to find the measure of a convex pentagon having an interior angle?
The sum of the interior angles in any convex polygon with [tex]$n$[/tex] sides is
[tex](n-2) \times 180^{\circ}$[/tex]
So, for a pentagon (which has 5 sides), its interior angles sum to
[tex]&(5-2) \times 180^{\circ} \\[/tex]
[tex]=& 3 \times 180^{\circ} \\[/tex]
[tex]=& 540^{\circ}[/tex]
We also know what each angle is, in terms of [tex]$x$[/tex].
Thus, we can equate the sum of all 5 angles to the angle sum of
[tex]$540^{\circ}$[/tex]:
[tex](5 x-12)+(2 x+100)+(4 x+16)+(6 x+15)+(3 x+41)=540$[/tex]
Combining like terms, we get
[tex]20 x+160=540$[/tex]
Now, solve the value of [tex]$\boldsymbol{x}$[/tex] :
[tex]&20 x=380 \\[/tex]
[tex]&x=19[/tex]
The value of [tex]&x=19[/tex].
To learn more about a convex pentagon
https://brainly.com/question/12229591
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