📐 geometry

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

1. **Problem Statement:** In triangle $\triangle ABC$, $DB$ and $AE$ are medians. Given: - $BE = 6y + 10$

1. **Problem statement:** Two cubes each with edge length 6 cm are joined end to end. We need to find the surface area of the resulting cuboid. 2. **Understanding the problem:** Ea

1. **Problem statement:** Given triangle ABC with sides AB = 7.2 cm, AC = 3.5 cm, and angle BAC = 28°, find the measure of angle ACB to the nearest degree. 2. **Formula used:** We

1. **Stating the problem:** We have triangle ABC with sides AB = 7.2 cm, AC = 3.5 cm, and angle BAC = 28°. We need to find the measure of angle ACB.

1. **State the problem:** We have a triangle with a base of 7 cm and two angles adjacent to the base: 40° and 20°. We need to find the length $x$ of the side opposite the base. 2.

1. **Problem b:** Find $x$ given angles $95^\circ$ and $125^\circ$ around a point. 2. **Step 1:** Recall that the sum of angles around a point is $360^\circ$.

1. **Problem Statement:** We are given a circle with points A, B, C, D on its circumference and angles marked as follows: \(\angle A = 55^\circ\) (right angle), \(\angle B = 39^\ci

1. **State the problem:** Find the volume of a right triangular prism where the base is a right triangle with one leg 5.7 cm, an adjacent angle of 42°, and the prism height (length