Question

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

Answer 1

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°

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°