Look at the parallelogram below and calculate the size of angle .
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Look at the parallelogram below and calculate the size of angle .
Since we are dealing with a parallelogram, there are 2 pairs of parallel lines.
As a result, we know that angle ADB and angle DBC are alternate angles between parallel lines and therefore both are equal to each other (44 degrees):
Now we can calculate angle ABC as follows:
Finally, let's substitute in our values:
84
Find the measure of the angle \( \alpha \)
Alternate interior angles are on opposite sides of a transversal (diagonal line) and between the parallel lines. In this problem, angle ADB and angle DBC are alternate interior because diagonal AC cuts through parallel sides.
You need to understand what each angle represents first. The 40° is angle ABD, and 44° is angle DBC. Since these are adjacent angles that together form angle ABC, you can add them: 40° + 44° = 84°.
Without the diagonal, you'd use different properties! Adjacent angles in a parallelogram are supplementary (sum to 180°), and opposite angles are equal. The diagonal helps us use alternate interior angle relationships.
Check that opposite angles are equal and adjacent angles sum to 180°. Since ∠ABC = 84°, then ∠ADC = 84° (opposite), and ∠ABC + ∠BCD = 84° + 96° = 180° ✓
Alternate interior angles are on opposite sides of the transversal and inside the parallel lines. Corresponding angles are on the same side of the transversal and in matching positions. Both are equal when lines are parallel!
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