Find the measure of M

∠M = 78º

∠N = 68º

∠P = 34º

Step-by-step explanation:

we know that the inside of a triangle is equal to 180º. we also know that angle p and angle q equal 180º when added together because that's the angle of a straight line. first we need to find angle p.

180 - 146 = 34º

now we can set it up so that all the angles equal 180º when added together.

(5y + 3) + (4y + 8) + 34 = 180

5y + 4y = 9y

9y + 3 + 8 + 34 = 180

3 + 8 + 34 = 45

9y + 45 = 180

    -45      -45

9y = 135

÷9      ÷9

y = 15

now we can plug 15 in for y

(5 x 15 + 3) = 78º

(4 x 15 + 8) = 68º

to double check, add all three angles and make sure they equal 180º

78 + 68 + 34 = 180

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2