Answer:
m∠H < m∠GIH < m∠G
IK < JK < IJ
Step-by-step explanation:
Theorem: Alternate angles are equal
m∠H = m∠J = 57°
Theorem: Sum of interior angles of a triangle is 180°
m∠G = 180 - m∠H - 60 = 180 - 57 - 60 = 63°
Theorem: Vertically opposite angles are equal
m∠GIH = m∠JIK = 60°
Therefore, m∠H < m∠GIH < m∠G
57 < 60 < 63
Theorem: The longest side in a triangle is opposite the largest angle, and the shortest side is opposite the smallest angle
∠K = 63°
∠JIK = 60°
∠J = 57°
Therefore, IK < JK < IJ
