Test 10 – Question 30

When they tell you that \overline{AD}\parallel \overline{BC}, they’re telling you that angle D is also 90°. And that means if you draw one more segment, straight down from point B to a new point E on \overline{AD}, you break the quadrilateral into a rectangle and a right triangle. Like so:

Now, we know in a rectangle, the opposite sides are congruent. That means the new segment \overline{BE} we drew has the same length as \overline{CD}. And because the question told us CD=\dfrac{1}{2}AB, it’s also true that BE=\dfrac{1}{2}AB.

So ABE is a right triangle, and its hypotenuse is twice as long as one of its legs. That’s a special right triangle! A 30°-60°-90°, to be precise.

BE is the short leg, so angle A will be the 30° angle. That means angle ABE measures 60°. We know angle ABC is 90°, so angle B from the original figure measures 150°.

Leave a Reply