📐 geometry

1. **State the problem:** We are given two angles formed by a transversal intersecting two parallel lines. The angles are \((100 - 2x)^\circ\) and \((10x)^\circ\). We need to solve

1. **State the problem:** We are given two angles formed by a transversal intersecting two parallel lines. The angles are \((100 - 2x)^\circ\) and \((10x)^\circ\). We need to solve

1. **State the problem:** We are given two angles formed by a transversal intersecting two parallel lines. The angles are \((100 - 2x)^\circ\) at point K and \((10x)^\circ\) at poi

1. **State the problem:** We are given two parallel lines EF and GH cut by a transversal CD, creating two corresponding angles: one at point I on EF measuring $7x - 4$ degrees, and

1. **State the problem:** We need to find the value of $x$ given two angles formed by a transversal intersecting two parallel lines. The angles are $(5x - 3)^\circ$ and $62^\circ$.

1. **State the problem:** We are given two angles formed by a transversal crossing two parallel lines. The angles are \((134 - 2x)^\circ\) and \((140 - 5x)^\circ\). We need to solv

1. The problem is to find the vertices of the intersection of two or more geometric shapes or functions. 2. Vertices are points where two or more edges or curves meet, often found

1. **Problem Statement:** We are given a pentagon ABCDE with the following properties: - AB = 7 cm

1. **State the problem:** We need to find the size of angle $\theta$ at vertex B in a triangle with sides AB = 52 cm, BC = 43 cm, and AC = 77 cm. 2. **Formula used:** To find an an

1. **State the problem:** We need to find the volume of a frustum formed by removing a smaller rectangular-based pyramid from a larger similar pyramid. 2. **Given dimensions:**

1. **Problem statement:** We need to find the volume of a frustum formed by removing a smaller rectangular-based pyramid from a larger similar pyramid. 2. **Given data:**

1. დავისახოთ პრობლემა: გვაქვს კვადრატი ABCD, სადაც AC არის დიაგონალი. 2. მოცემულია, რომ AF = 3 და FE = 1, გვინდა გავარკვიოთ EC-ის სიგრძე.

1. **Problem statement:** We have a regular hexagon ABCDEF with all sides 4 cm and center O.

1. **Problem statement:** We have a circle with a tangent line CDE touching the circle at point D. We need to find the sizes of angles $x$ and $y$ on the tangent line, given some a

1. Problem 1: Calculate the radius of a circle sector with central angle 133° and arc length 246 cm. Formula: Arc length $s = r \theta$ where $\theta$ is in radians.

1. **State the problem:** We need to find the coordinates of point Q(2, 3) after two reflections: first in the x-axis, then in the y-axis. 2. **Recall reflection rules:**

1. **Problem statement:** In triangle $ABC$, points $D$ and $E$ lie on sides $AC$ and $BC$ respectively. Given $BE=4$, $EC=10$, $AD=x$, and $DC=11$, find $x$ such that $DE \paralle

1. **State the problem:** We need to find the unknown angles $x$, $y$, and $w$ in the given triangles. 2. **Given information:**

1. **Problem Statement:** Determine which of the given shapes (A, B, C, D) are nets of cubes. 2. **Understanding Cube Nets:** A cube has 6 faces, each a square. A net of a cube is

1. **State the problem:** We are given a triangle with angles 26°, 34°, and 62°, and two unknown angles labeled $x^\circ$ and $y^\circ$. We need to find the measures of $x$ and $y$

1. **Problem statement:** A cone and a cylinder have the same base radius and volume. Find the ratio of the height of the cone to the height of the cylinder. 2. **Formula for volum