Let's use a formula in order to find how much the interior angles are supposed to add up to.
(n-2)×180; n is the number of angles.
(5-2)×180= 3×180=540
We need for the interior angles to add up to 540. Let's make an equation.
100+102+108+121+x=540
431+x=540; let's find x.
540-431= 109
So, X= 109°
very simple, we use the formula sin(a+b)=sinacosb +
sinbcosa and sin(20)=2sinacosa
5pi = 2pi/3+3pi/3,
First, we use sin(a+b)=sinacosb + sinbcosa
sin(5pi/3)=sin(2pi/3+3pi/3)=
sin(2pi/3+pi)=
sin(2pi/3)cos(pi) +sin(pi)cos(2pi/3)
but we know that sin(pi)=
0, and cos (pi) = -1, so sin(5pi/3)=
- sin(2pi/3)
now, use sin(2a)=2sinacosa,
sin(5pi/3)= - sin(2pi/3)= -2sin(pi/3)cos(pi/3)
sin<span>(5pi/3)=
-2sin(pi/3)cos(pi/3)</span>
<span>sin(pi/3)= 0.86,
cos(pi/3)=0.5, finally we have </span>sin<span>(5pi/3)= -0.86 x 0.5= -0.43</span>
x= number of boys in the club because it is unknown.
x + 7= the number total number of girls in the club.
