📐 geometry

1. **Problem Statement:** We have two intersecting lines forming angles. One angle is given as 34°. Angle $x$ is marked as a right angle, so $x = 90^\circ$.

1. **State the problem:** We have two similar triangles \(\triangle QRS \sim \triangle TUV\) and need to find the value of \(k\), the side length \(UV\) in \(\triangle TUV\). 2. **

1. **State the problem:** We have two similar triangles \(\triangle GHI \sim \triangle JKL\) with corresponding sides \(GI = 2\), \(HI = 6\), \(GH = 5\) and \(JL = 12\), \(JK = 30\

1. **State the problem:** We need to find the value of $x$ given the pentagon's interior angles: $125^\circ$, $(x + 7)^\circ$, $107^\circ$, $(x - 15)^\circ$, and $131^\circ$. 2. **

1. **State the problem:** We are given a pentagon with interior angles labeled as 125°, (x + 7)°, 107°, (x - 15)°, and 131°. We need to find the value of $x$. 2. **Recall the formu

1. **State the problem:** We have a square pyramid with a base area of 64 cm² and a slant height of 9 cm. We need to find the height $a$ of the pyramid. 2. **Recall formulas:**

1. **State the problem:** Brogan wants to position a coin so that it completely blocks her view of the Sun. We know: - Diameter of coin $d_c = 28$ mm

1. **State the problem:** Rowan wants to enlarge a shape using the origin $O$ as the center. The ratio of the length $OA$ to the length $OA'$ is $2:1$. Given point $A$ at coordinat

1. **State the problem:** We have a triangle with angles 60°, (2x + 9)°, and (4x + 3)°. We need to find the value of $x$. 2. **Recall the triangle angle sum rule:** The sum of the

1. **State the problem:** We have a cylinder of sherbet with height 32 cm and diameter 20 cm (radius 10 cm). The sherbet is poured into 250 conical containers each with diameter 5

1. **State the problem:** We are given a straight road with stop signs at both ends and a fire hydrant at its midpoint. The fire hydrant is at point $(12,7)$ and one stop sign is a

1. **State the problem:** Find the length of the line segment WX with endpoints W(-5,-1) and X(2,6). 2. **Formula used:** The distance between two points $(x_1,y_1)$ and $(x_2,y_2)

1. **State the problem:** Find the area of the given polygon with specified side lengths. 2. **Analyze the figure:** The polygon is a stepped shape with vertical and horizontal edg

1. **Stating the problem:** We are given a cuboid with a base rectangle having sides 4 cm and 19 cm, and a diagonal inside the base rectangle measuring 21 cm. We need to verify if

1. The problem is to understand the shape of the moon during its first or last quarter phase, which resembles a crescent shape. 2. The crescent moon shape can be modeled mathematic

1. **Problem statement:** We are given a triangle with vertices A, B, C, and a point D on the baseline from A to D. The angle at vertex B is $128^\circ$. We need to calculate the s

1. **State the problem:** We need to find the size of angle $BCD$ in the given figure. 2. **Analyze the given information:** The angle at vertex $B$ is given as $128^\circ$.

1. **State the problem:** We need to find the volume of a triangular prism with a triangular base of base length 7 m and height 4 m, and the prism length (depth) is 8 m. 2. **Formu

1. **State the problem:** Find the volume of a prism. 2. **Formula:** The volume $V$ of a prism is given by the formula:

1. **State the problem:** Find the volume of a right triangular prism with a base triangle having legs 10 cm and 4 cm, and a prism depth of 2 cm. 2. **Formula:** The volume $V$ of

1. **State the problem:** We need to find the coordinates of the vertices of triangle FGH after a 90° counterclockwise rotation around the origin. 2. **Recall the rotation formula: