ATLAS Geometry Congruence. Practice it free.

The three interior angles sum to $180°$: $(x+8)+(2x+17)+(x+55)=180$, so $4x+80=180$ and $x=25$.

A rotation is a rigid transformation that turns a figure around a fixed point, called a center of rotation, by a specific angle in a specific direction. All points remain equidistant from the center of rotation, keeping the image congruent to the preimage.

Corresponding angles are congruent: $3x+16=2x+34$, so $x=18$. Each angle measures $3(18)+16=70°$.

A translation is a rigid transformation that moves every point of a figure the exact same distance in the same direction. Since all points in the image remain equidistant from the points in the preimage, the figure remains congruent.

Same-side interior angles are supplementary: $(6x-5)+(4x+15)=180$, so $10x+10=180$ and $x=17$.

A reflection is a rigid transformation that maps the points from a preimage, over a line of reflection, to the points of an image that are equidistant to the line. In this example, that line is the perpendicular bisector of a line segment from a point to its image, so the segment maps onto itself.

A linear pair is supplementary: $(5x+10)+(3x+50)=180$, so $8x+60=180$ and $x=15$. The angles are $85°$ and $95°$, so the larger is $95°$.

A rotation is a rigid transformation that turns a figure around a fixed point, called a center of rotation, by a specific angle in a specific direction. All points remain equidistant from the center of rotation, keeping the image congruent to the preimage. In this example, that angle is $80^{\circ}\textsf{.}$