1. A pair of supplementary angles: ∠IJH and ∠HJG, ∠IJH and ∠HJG
2. A pair of complementary angles: ∠JGK and ∠KGC, ∠FGE and ∠EGD
3. A pair of vertical angles: ∠AKB and ∠KJG , ∠IJH and ∠KJG
Solution:
Two angles are said to be supplementary when they add up to 180°.
We know that,
Sum of the adjacent angles in a straight line = 180°
∠IJK + ∠KJG = 180°
Therefore ∠IJK and ∠KJG are supplementary angles.
∠IJH + ∠HJG = 180°
Therefore ∠IJH and ∠HJG are supplementary angles.
Two angles are said to be complementary when they add up to 90°.
Given ∠CGD = 90°, ∠CGJ = 90°
∠JGK + ∠KGC = ∠CGJ
∠JGK + ∠KGC = 90°
Therefore ∠JGK and ∠KGC are complementary angles.
∠FGE + ∠EGD = 90°
Therefore ∠FGE and ∠EGD are complementary angles.
If two lines are intersecting, then the angles opposite to vertical point are vertical angles and they are equal.
∠AKB = ∠KJG (vertically opposite)
∠IJH = ∠KJG (vertically opposite)