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.

Translations preserve all angle measures, including both interior and exterior angles. The exterior angle at vertex C measures 72°, so the exterior angle at the corresponding vertex in the translated hexagon also measures 72°. Choice B incorrectly gives the supplementary angle. Choice C incorrectly suggests the translation affects angle measures. Choice D incorrectly claims the measure cannot be determined.

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.

When you see questions about transformations and angle measures, remember that translations and reflections are rigid transformations—they preserve all angle measures and side lengths of the original figure.

Let's work through this step-by-step. First, you need to find all angles in the original triangle ABC. Since the sum of angles in any triangle is $$180°$$, and you know two acute angles measure $$35°$$ and $$55°$$, the third angle must be $$180° - 35° - 55° = 90°$$. This means triangle ABC is a right triangle.

Now apply the transformations. When triangle ABC is translated 5 units right and 7 units up, all angles remain unchanged: $$35°$$, $$55°$$, and $$90°$$. When triangle A'B'C' is reflected across the x-axis, the angles again stay the same: $$35°$$, $$55°$$, and $$90°$$. The largest angle in triangle A''B''C'' is $$90°$$.

Looking at the wrong answers: Choice A ($$55°$$) is the measure of one of the acute angles, not the largest angle. Choice B ($$125°$$) might tempt you if you mistakenly thought one angle changed during transformation, but this value doesn't correspond to any angle in the triangle. Choice D ($$145°$$) is also impossible since it would make the triangle's angle sum exceed $$180°$$.

Remember this key principle: rigid transformations (translations, reflections, rotations) never change angle measures or side lengths. When you see transformation problems asking about measurements, the answer will always be the same as in the original figure.

When you encounter questions about rotations and angle measures, remember that rotations are rigid transformations - they preserve all distances, angles, and shapes exactly as they were in the original figure.

The key insight here is that rotating a parallelogram doesn't change any of its interior angles or their sum. Whether the parallelogram is rotated 45°, 90°, or any other amount, and whether the center of rotation is inside, outside, or on the parallelogram, the shape itself remains identical to the original. The rotation simply moves the entire figure to a new position.

Since we know the original parallelogram has opposite angles measuring 115° and 65°, and opposite angles in a parallelogram are always equal, the four angles are: 115°, 65°, 115°, and 65°. These sum to $$115° + 65° + 115° + 65° = 360°$$. After rotation, these same four angles still sum to 360°.

Looking at the wrong answers: A) 315° might seem tempting if you mistakenly subtracted the 45° rotation angle from 360°, but rotations don't affect interior angle measures. B) 405° could result from incorrectly adding the rotation angle to 360°, again showing a misunderstanding of how rotations work. D) suggests that the location of the rotation center matters for angle measures, which is false - only the position of the figure changes, not its geometric properties.

Remember: rigid transformations (rotations, reflections, translations) never change angle measures, side lengths, or area. The sum of interior angles in any quadrilateral is always 360°.

Under translations, angles map to angles of the same measure. First, find angle BCD: if angle ABC + angle BCD = 195° and angle ABC = angle BCD + 25°, then (angle BCD + 25°) + angle BCD = 195°, so 2(angle BCD) = 170°, giving angle BCD = 85°. Since translations preserve angle measures, angle B'C'D' (corresponding to angle BCD) measures 85°. Choice B gives the measure of angle ABC instead. Choice C might result from adding the 25° difference incorrectly. Choice D gives the sum of both angles.

Under rotations, angles map to angles of the same measure, regardless of the degree of rotation. The 124° angle formed by the intersecting diagonals maps to the corresponding angle in the rotated rectangle, which also measures 124°. Choice A gives the supplement of 124°. Choice C incorrectly adds the rotation angle to the original angle. Choice D reflects the misconception that the degree of rotation affects angle preservation.

Under rotations, angles map to angles of the same measure. First, we find angle ACB in the original triangle: 180° - 42° - 73° = 65°. Since rotations preserve angle measures, angle A'C'B' (which corresponds to angle ACB) also measures 65°. Choice A incorrectly matches angle A'C'B' with angle BAC. Choice C incorrectly matches it with angle ABC. Choice D confuses the rotation angle with an interior angle of the triangle.

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.