Question

In the given figure AB || DC, AD || BC ∠D = 52° and ∠BCE = 28°. ∴ ∠E is ______.

Options

• 30°

• 28°

• 24°

• 38°

Answer 1

In the given figure AB || DC, AD || BC ∠D = 52° and ∠BCE = 28°. ∴ ∠E is 24°.

Explanation:

We are given a parallelogram ABCD with an extended line CE

• AB || DC, AD || BC
• ∠D = 52°
• ∠BCE = 28°

We are to find:

∠E (i.e. ∠CBE)

Step-by-step:

1. Since ABCD is a parallelogram, opposite angles are equal:

∠D = ∠B = 52°

2. In triangle ΔCBE:

• ∠BCE = 28°   ...(Given)
• ∠CBE = ∠E   ...(What we want)
• ∠B = 52°, which is the interior angle adjacent to ∠CBE

3. Use angle on a straight line:

∠E = 180° – ∠B – ∠BCE

∠E = 180° – 52° – 28° = 100°   ...(This is incorrect logic!)

In triangle ΔCBE:

• ∠BCE = 28°
• ∠B = 52° ⇒ So, ∠CBE = 180° – 52° = 128°   ...(Linear pair)
• Now, triangle angles sum to 180°:
  ∠CBE = 128°
  ∠BCE = 28°
  ⇒ ∠E = 180° – 128° – 28° = 24°