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

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°.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

  answer:

  write 548 as 500 + 40 + 8. multiply each addend by 5. then add the three products to get 2,740.