Test 10 – Question 30

When they tell you that , they’re telling you that angle is also 90°. And that means if you draw one more segment, straight down from point to a new point on , 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 we drew has the same length as . And because the question told us , it’s also true that .

So 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.

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