Answer:
4. x = 42, y = 138, z = 9
5. x = 4
6. x = 63, y = 8
Explanation:
Corresponding angles are congruent in similar figures. Corresponding sides have the same ratio.
4. The acute angle is shown to have measure 42°. x° is the measure of the acute angle, so x = 42.
The angles made by one side of a trapezoid with the bases are supplementary, so y° = 180° -42° = 138°. y = 138.
The sides marked 8 in the larger trapezoid are marked 6 in the smaller one, so its sides are 6/8 = 3/4 of those of the larger trapezoid. That means the side marked z is 3/4 of the corresponding side marked 12 in the larger trapezoid. z = 3/4×12 = 9.
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5. The short side (2) of the smaller rectangle is half the length of the longer side (4) in that same rectangle. That means the short side (x) will be half the length of the longer side (8) in the larger similar rectangle.
x = 8/2 = 4
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6. Corresponding angle are congruent, so the acute angle adjacent to the short side will be 63°. x = 63.
The short side (4) is half the length of the long side (8) in the smaller triangle, so the same will be true in the larger one. The short side (y) is half the length of the long side (16).
y = 16/2 = 8