Question

if ray NP bisects angle MNQ and measure of angle MNQ= 8x + 12 and measure of PNQ= 78 degrees and measure of angle RNM= 3y -9, find the values of x and y

Answer 1

(8x+12)+(3y-9)= 8x+3y+3=78

subtract 3 from both sides

8x+3y=78

subtract 8x from both sides

3y=-8x+78

divide both sides by 3

y=-8/3x+26 or y=-2.666666666x+26

substitute for y

8x+3(-8/3)+26=78

subtract the 26 from both sides

8x+3(-8/3)=52

distribute the 3

8x- 7.99999999998=52

add the -7.999999999998 to bother sides

8x=60

divide both sides by 8

x=7.5

substitute for x

8(7.5)+3y=78

60+3y=78

subtract 60 from both sides

3y=18

divide both sides by 3

y=6

so x=7.5 and y=6