ABCD is a rectangle.
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ABCD is a rectangle.
Since we know that ABCD is a rectangle, we know that AC is parallel to BD.
Therefore, angles ACB and CBD are equal (30 degrees).
In a rectangle, we know that all angles are equal to 90 degrees, meaning angle ABD is equal to 90.
Now we can calculate angle ABC as follows:
60
Look at the angles shown in the figure below.
What is their relationship?
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The diagonal AC creates alternate interior angles with the parallel sides of the rectangle. Since ABCD is a rectangle, opposite sides are parallel, making .
In any rectangle, all four corner angles are 90°. So angle ABD (which is the same as angle ABC plus angle CBD) must equal 90°.
Angle ABD is the full corner angle of the rectangle (90°). Angle ABC is just part of that corner, from side AB to the diagonal AC.
Yes! You can also use the fact that in rectangle ABCD, (complementary angles in a right triangle). So .
The marked 30° is angle ACB, not angle ABC! Always read the diagram carefully to identify which angle is actually being asked for in the question.
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