Question

Find the value of x for which ABCD must be a parallelogram.

Answer 1

The value of x is 13°.

Solution:

Given ABCD is a parallelogram.

⇒ AD || BC and AC is a transversal line.

Property of parallel lines:

If two parallel lines cut by a transversal, then the alternate interior angles are equal.

∠DAC = ∠CAB

(4x - 1)° = (x + 38)°

4x° - 1° = x° + 38°

Add 1° on both sides.

4x° - 1° + 1° = x° + 38° + 1°

4x° = x° + 39°

Subtract x° from both sides.

4x° - x° = x° + 39° - x°

3x° = 39°

Divide by 3° on both sides.

x = 13°

The value of x is 13°.