Answer:
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°
