Recall that each angle in a square is 90°.

Looking at the diagram, we have 3 overlapping squares.

We can see that :

∠a + ∠b + ∠c = 90° (left square)
∠d + ∠b + ∠c = 90° (middle square)

So comparing the two,

∠a = ∠d


Likewise,

∠b + ∠c + ∠d = 90° (middle square)

∠e + ∠c + ∠d = 90° (right square)


So comparing the two,

∠b = ∠e



Another way to think about it :

We can get to the middle square by rotating the left square rightwards.

Pushing it up by ∠a results in an extension by ∠d on its other side.

So the two angles are equal.



We can get to the middle square by rotating the right square leftwards.


Pushing it up by ∠e results in an extension by ∠b on its other side.

So the two angles are equal.

b)

∠a + ∠b
= 90° - ∠c
= 90° - 15°
= 75°

∠c + ∠d + ∠e = 90°
(as seen from the diagram)

So,

∠a + ∠b + ∠c + ∠d + ∠e

= 75° + 90°
= 165°


Or



∠d + ∠e
= 90° - ∠c
= 90° - 15°
= 75°

∠a + ∠b + ∠c = 90°
(as seen from the diagram)

So,

∠a + ∠b + ∠c + ∠d + ∠e

= 90° + 75°
= 165°

Alternatively for b) ,


∠a + ∠b + ∠c + ∠d + ∠e

= 1 angle of left square + 1 angle of right square - overlapping ∠c

(we cannot double count ∠c)


= 90° + 90° - 15°

= 180° - 15°

= 165°


Or


90° × 2 - 15°

= 180° - 15°

= 165°