Which of the pairs of angles are complementary? ∠apb and ∠zpb ∠apz and ∠bpz ∠apw and ∠zpw ∠wpz and ∠bpz

∠APW and ∠ZPW

Step-by-step explanation:

Pair of complementary angles : A pair of angles whose sum is 90° is said to be the pair of complementary angles.

Option 1 : ∠APB and ∠ZPB

Since APB is straight line

So, ∠APB = 180°

∠ZPB = 90°(Given)

So, ∠APB +∠ZPB=180°+ 90°= 270°

Since the sum of angles is not 90°.

Thus Option 1 is not a pair of complementary angles.

Option 2: ∠APZ and ∠BPZ

∠APZ = 90°

∠BPZ = 90°

So, ∠APZ +∠BPZ =90°+90° =180°

Since the sum of angles is not 90°.

Thus Option 2 is not a pair of complementary angles.

Option 3 : ∠APW and ∠ZPW

∠APW+∠ZPW=∠APZ

∠APZ =90°(Given)

So,∠APW+∠ZPW=90°

Since the sum of angles is 90°.

Thus Option 3 is  a pair of complementary angles.

Option 4: ∠WPZ and ∠BPZ

∠WPZ + ∠BPZ =  ∠WPZ + 90°

Since the sum of angles must be greater than 90°.

Thus Option 4 is not a pair of complementary angles.

Hence ∠APW and ∠ZPW are the pair of complementary angles.

a. is correct