Find the unknown angle measure: ..not sure if child's answers are correct?

Part 1) The measure of angle PSL is 45°

Part 2) The measure of angle XYZ is 70°

Part 3) The measure of angle HJZ is 100°

Part 4) The measure of angle PHL is 120°

Part 5) The measure of angle WXZ is 140°

Part 6) The measure of angle UTG is 62°

Step-by-step explanation:

Part 1) Find the measure of angle PSL

we know that

∠PSL+∠LSM=90° > by complementary angles

we have

∠LSM=45°

substitute

∠PSL+45°=90°

∠PSL=45°

Part 2) Find the measure of angle XYZ

we know that

∠WYX+∠XYZ=180° > by supplementary angles

we have

∠WYX=110°

substitute

110°+∠XYZ=180°

∠XYZ=70°

Part 3) Find the measure of angle HJZ

we know that

∠HJZ=∠HJK+∠KJZ

we have

∠HJK=20°

∠KJZ=80°

substitute

∠HJZ=20°+80°=100°

Part 4) Find the measure of angle PHL

we know that

∠PHL=∠PHS+∠SHL

we have

∠PHS=46°

∠SHL=74°

substitute

∠PHL=46°+74°=120°

Part 5) Find the measure of angle WXZ

we know that

∠WXZ=∠WXY+∠YXZ

we have

∠WXY=15°

∠YXZ=125°

substitute

∠WXZ=15°+125°=140°

Part 6) Find the measure of angle UTG

we know that

∠UTG=∠ATG-∠ATU

we have

∠ATG=120°

∠ATU=58°

substitute

∠UTG=120°-58°=62°

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)