📐 geometry

1. **State the problem:** We need to find the number of sides $n$ of a regular polygon given that each interior angle measures 172°. 2. **Formula for interior angle of a regular po

1. **State the problem:** We have a scale drawing of a motel where 6 inches on the drawing corresponds to 30 yards in actual length. The east side of the motel measures 2 inches on

1. **State the problem:** We have a convex polygon with six interior angles given as: - 131°

1. **Problem:** Name the geometric solid formed when a right triangle is rotated around the x-axis. The solid formed is a **cone** because rotating a right triangle around one of i

1. **State the problem:** Chani starts with point $S(-8,6)$ and applies two transformations: a translation right 5 units, then a 180° rotation around the origin.

1. **State the problem:** Duncan is transforming point $S(1,0)$ by translating it down 3 units, then reflecting over the x-axis. We need to check if Duncan's work is correct. 2. **

1. **State the problem:** We have a right triangle with angles 30°, 60°, and 90°. The side opposite the 60° angle (the hypotenuse) is 5 inches, and we need to find the length of si

1. The problem asks for the coordinate notation representing a translation left 5 units followed by a 180 degree rotation around the origin. 2. Translation left 5 units means subtr

1. The problem asks to find the coordinate notation that represents a translation up 1 unit followed by a reflection over the x-axis. 2. Translation up 1 unit means adding 1 to the

1. The problem asks to find the coordinate notation for a translation up 1 unit followed by a reflection over the x-axis. 2. Translation up 1 unit means adding 1 to the y-coordinat

1. **State the problem:** We have a right triangle with angles 30º, 60º, and 90º. The side opposite the 30º angle is given as $9\sqrt{3}$ mm, and we need to find the length $c$ opp

1. **State the problem:** We have a right triangle with angles 45°, 45°, and 90°, and the hypotenuse is given as $6\sqrt{2}$ meters. We need to find the length of side $g$ adjacent

1. **State the problem:** We need to identify which image shows the preimage rotated 270 degrees counterclockwise around the origin. 2. **Recall the rotation rule:** A rotation of

1. **State the problem:** We need to find the coordinates of point A after two transformations: a translation right 6 units followed by a reflection over the y-axis. 2. **Identify

1. **State the problem:** We need to find the size of angle $x$ in a right-angled triangle where the opposite side to $x$ is 8.6 cm and the adjacent side to $x$ is 3.8 cm. 2. **For

1. **Stating the problem:** We have a prism with a cross-sectional shape of a sector of a circle. The sector has radius $r$ cm, central angle $50^\circ$, the prism length is 20 cm,

1. **Problem Statement:** We have a rectangle AUNT with dimensions $AU=6$ cm (width) and $UN=3$ cm (height). Point $J$ lies on the line extended from the bottom edge $NT$ but outsi

1. **Problem statement:** A closed cylindrical oil can must hold a volume of 1 litre (1000 cm³). We want to find the dimensions (radius $r$ and height $h$) that minimize the surfac

1. **Stating the problem:** We have a triangle with sides labeled 15, 12, and a top side divided into segments 10, $y$, and $x$. There is also a segment of length 4 parallel to the

1. **State the problem:** We have two parallel vertical lines \(\ell, m, n\) and two parallel horizontal lines intersecting them, forming segments. The top horizontal line has segm

1. **State the problem:** Find the distance between the points $(6,5)$ and $(7,8)$. 2. **Formula used:** The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by