This question tests understanding that rotations preserve angle measures, even with 180° turns. Angle ABC=90° rotated 180° about B forms A'B'C'=90° unchanged. Example: 90° rotated 180° stays 90°. Specifically, after 180° rotation, the image measures 90°. Correct preservation: remains 90°, as isometry. Errors: thinking it becomes 180° or 270° by adding. Verification: original 90°, apply 180° rotation, image 90°, preserved; orientation changes but measure same.

This question tests understanding that translations preserve angle measures by shifting without changing size. Angle STU=45° is translated 10 units left to form S'T'U' with the same 45° measure, as position change doesn't affect ray spread. Example: 90° translated left remains 90°. Specifically, after left shift, the image angle measures 45°. It is the same because translation preserves angle measure. Errors: thinking movement left increases/decreases measure or makes rays separate to 0°. Verification: original 45°, apply translation, image 45°, preserved; rigid transformations maintain angles via isometry.

This question tests understanding that reflections preserve angle measures in triangles, as rigid transformations maintain all angles. Triangle PQR with angles 40°, 60°, 80° is reflected to form P'Q'R' with the same 40°, 60°, 80° measures, unchanged despite flipping. For example, a triangle with 90°, 45°, 45° reflected keeps those exact angles. Specifically, after reflection, P'Q'R' has angles 40°, 60°, 80°, as individual measures are preserved. Correctly, the set of angles remains identical, summing to 180° before and after. Errors: thinking reflection alters angles to new sets like 40°, 60°, 90°. Verification: original angles 40°,60°,80°, apply reflection, image angles same, preserved; multiple angles stay exact under isometries.

This question tests understanding that reflections preserve individual angle measures, keeping relationships like supplementary. Angles 110° and 70° are reflected to 110° and 70°, still supplementary as measures are unchanged. Example: 90° and 90° reflected remain 90° each. Specifically, after x-axis reflection, ∠1'=110° and ∠2'=70°, summing to 180°. True statement: they are 110° and 70°, still supplementary. Errors: thinking reflection swaps or changes to non-supplementary. Verification: originals 110°,70°, apply reflection, images same measures, preserved; relationships hold due to isometry.

This question tests understanding that rotations, rigid transformations, preserve angle measures by turning the figure but not altering angle sizes. Angle JKL with measure 90° is rotated 45° counterclockwise about K to form angle J'K'L' with measure 90° unchanged, as rotation affects orientation but not the ray spread. Example: a 90° angle rotated 45° remains 90°, just pointing differently. Here, rotating the right angle 45° CCW about the vertex keeps the measure at 90° in the image. Correctly, the image angle equals the original due to rotation's isometry property. Common mistakes: adding rotation amount to the measure (90° +45°=135°), thinking it changes size. Verification: original 90°, apply 45° rotation, image measures 90°, preserved; angles depend on preserved distances.

This question tests understanding that reflections preserve angle measures, not flipping to supplements. Angle GHI=60° reflected forms G'H'I'=60°, unchanged despite flip. Example: 90° reflected stays 90°. Specifically, the image angle is 60°. Incorrect; still 60° because reflection preserves measure. Errors: claiming it becomes supplement (120°) or 0°. Verification: original 60°, apply reflection, image 60°, preserved; mistakes like confusing flip with size inversion.

This question tests understanding that reflections, a rigid transformation, preserve angle measures by flipping the figure but not changing angle sizes. Angle DEF with measure 120° is reflected across the y-axis to form angle D'E'F' with measure 120° unchanged, whether flipped or not, as the spread between rays remains the same. For instance, a right angle of 90° reflected over an axis is still 90°, oriented differently but with the same measure. Specifically, reflecting angle DEF=120° over the y-axis changes coordinates (e.g., points mirror), but measuring the angle at the new vertex gives 120°. The correct preservation is that the image angle equals the original, as reflections are isometries. Errors include claiming reflection inverts the measure (e.g., 120° becomes -120° or 60°), confusing sign with size. Verification: original 120°, apply reflection, image measures 120°, preserved; all rigid transformations maintain angles via distance preservation.

This question tests understanding that translations, a type of rigid transformation, preserve angle measures by changing position but not the size or shape of the angle. Angle ABC with measure 50° is translated to form angle A'B'C' with measure 50° unchanged, as translation simply shifts the angle without altering the spread between its rays. For example, a right angle of 90° translated horizontally remains 90°, just in a new location but with identical measure. In this specific case, translating angle ABC=50° by 6 units right and 2 units up results in angle A'B'C'=50°, as the coordinates change but the angle at the vertex stays the same. The correct answer is that the measure is preserved at 50°, a property of rigid transformations. A common error is thinking translation affects angles, like adding the shift amounts to the measure (e.g., 50° + 6° + 2° =58°), but it doesn't change the 'openness'. To verify, measure original angle ABC=50°, apply translation to points, measure image angle A'B'C'=50°, confirming preservation since distances are maintained.

This question tests understanding that rotations preserve angle measures, not adding or changing them. Angle MNO=30° is rotated 90° clockwise about N to form M'N'O' with 30° unchanged, as rotation preserves the spread. Example: 90° rotated 45° stays 90°. Specifically, after 90° rotation, the image angle is still 30°. The true statement is that it remains 30° because rotation preserves measure. Errors: adding rotation to angle (30°+90°=120°), thinking it doubles or makes obtuse. Verification: original 30°, apply 90° rotation, image 30°, preserved; mistakes like confusing rotation amount with measure.

This question tests understanding that rotations, reflections, and translations preserve angle measures—rigid transformations change position or orientation but not angle size. Angle measure is preserved under rigid transformations: any angle transforms to an image with the same measure (unchanged) whether rotated (turned), reflected (flipped), or translated (shifted). The measure depends on the spread between rays forming the angle, not position or orientation—moving or rotating the angle doesn't change the 'openness' or degree measure. For example, a right angle (90°) rotated 45° is still 90°, now oriented differently but measure identical. The true statement is that all rigid transformations preserve angle measures, as they are isometries. Errors include claiming only rotations preserve or reflections change acute to obtuse, ignoring that all maintain measures. Verification: consider any angle, apply each transformation, measures match; all preserve distances, thus angles.