ABCD is a quadrilateral.
AB||CD
AC||BD
Calculate angle .
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ABCD is a quadrilateral.
AB||CD
AC||BD
Calculate angle .
Angles ABC and DCB are alternate angles and equal to 45.
Angles ACB and DBC are alternate angles and equal to 45.
That is, angles B and C together equal 90 degrees.
Now we can calculate angle A, since we know that the sum of the angles of a square is 360:
90°
Find the measure of the angle \( \alpha \)
Parallel lines create special angle relationships! When lines are parallel, alternate angles are equal and corresponding angles are equal. These relationships help us find exact angle measures.
The parallel conditions AB||CD and AC||BD, combined with the 45° alternate angles shown, create four right angles. This makes ABCD a rectangle where all angles equal 90°.
Alternate angles are angles on opposite sides of a transversal crossing parallel lines. They're always equal because parallel lines never meet, creating identical angle relationships.
No! With the given constraints (AB||CD, AC||BD, and the 45° markings), the quadrilateral must be a rectangle. All angles in a rectangle are exactly 90°.
Those 45° angles are alternate angles, not the interior angles of the quadrilateral! They help us determine that angles B and C each equal 90°, which then helps find angle A.
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