(I have an attachment so you know what the problem looks like)

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)

x = 12

y = 1

for the points!