Find the value of x for which ABCD must be a parallelogram.
1 answer:
The value of x is 13°.
Solution:
Given ABCD is a parallelogram.
⇒ AD || BC and AC is a transversal line.
<u>Property of parallel lines: </u>
<em>If two parallel lines cut by a transversal, then the alternate interior angles are equal. </em>
∠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°.
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