Test 10 – Question 30 – PWN Test Prep

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°.

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