Answer:
- ∠PQR measures 40°
- x = 7
- They form concentric circles
- Yes, according to the triangle inequality
Step-by-step explanation:
1. ∠PQR is an alternate interior angle with the one marked 40°, so it has the measure 40°.
∠PRQ is an alternate interior angle with the one marked 60°, so it has the measure 60°.
Among the answer choices, the one describing ∠PQR as 40° is the only correct one.
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2. ∠BAD = 2×∠BAE
130 = 2(9x + 2) . . . substitute the given expressions
65 = 9x + 2 . . . . . divide by 2
63 = 9x . . . . . . . . .subtract 2
7 = x . . . . . . . . . . . .divide by 9
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3. Think again. Anything being rotated follows a circular path. Circular paths with different radii and the same center are concentric circles.
Straight lines connecting the pre-image and image points will be parallel (and different lengths), but the question is concerned with paths, not endpoints.
Why the path is described as "concentric circles," we're not sure. The path for a 90° rotation will be a 90° arc. It is perfectly reasonable to describe the paths of the two points as concentric arcs, rather than concentric circles. See the attachment.
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4. Correct. The triangle inequality requires the sum of the two shortest side lengths exceed the longest side length. Here, that means 2+5 > 5 (true). The "toothpicks" meet the requirements of the triangle inequality, so will make a triangle.
The "triangle sum theorem" has to do with angles, not side lengths.
