📐 geometry

1. The problem is to find the values of angles $x$, $y$, and $z$ given the angles $40^\circ$, $121^\circ$, and the variables $x^\circ$, $y^\circ$, $z^\circ$. 2. We use the rule tha

1. **State the problem:** Jessica's eyes are 175 cm above the floor. She places a mirror on the ground 650 cm away from a flagpole. She then walks back 1 meter (100 cm) until she s

1. **State the problem:** Calculate the distance $d$ between two points using the distance formula. 2. **Distance formula:** The distance between points $(x_1, y_1)$ and $(x_2, y_2

1. **State the problem:** We are given a sector OAB of a circle with radius $r = 4.6$ mm and sector area $A = 18$ mm². We need to find the central angle $\theta$ in degrees to 1 de

1. **Stating the problem:** We are given a trapezoid IJKL with two bases IJ and LK expressed in terms of $x$, and a median MN with length 15. We need to find the value of $x$ and t

1. **Stating the problem:** Identify which two lines among m, n, o, p, and q are parallel based on the given figure and definitions. 2. **Definition:** Parallel lines are lines in

1. **State the problem:** We need to find the area of the minor sector OAB of a circle with radius $40$ cm and central angle $36^\circ$. 2. **Formula for the area of a sector:** Th

1. **Problem statement:** Given a circle with diameter QIT and angles \(\angle QIT = 48^\circ\), \(\angle TQR = 70^\circ\), and \(\angle MCI = 17^\circ\), find the sizes of the fol

1. **Problem Statement:** We have a solid composed of a conical frustum with a hemispherical top. Given:

1. **Problem statement:** We have a solid made of a conical frustum with a hemispherical top. Given:

1. **Problem:** Find the length of the angle indicated for trapezoid 1, where angle at S is 65° and angle at R is unknown. 2. **Formula and rules:** In a trapezoid, consecutive ang

1. **State the problem:** We need to find the perimeter of an irregular polygon shaped like a rotated letter "E" with given side lengths. 2. **Identify the given sides:** The polyg

1. Stating the problem: Generate a similar exercise involving a composite figure made of a rectangle and two semicircles but with different measurements. 2. Original figure details

1. **Problem Statement:** We have a solid made of a conical frustum with a hemispherical top. Given:

1. The distance formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$

1. **Problem Statement:** Find the missing value of Surface area ÷ Volume for a cube stack with 27 cubes.

1. The problem is to find the distance between two points in a plane using the distance formula. 2. The distance formula between points $A(x_1,y_1)$ and $B(x_2,y_2)$ is:

1. **Problem:** On a circle of radius 10 m, find the length of an arc subtending a central angle of (a) $\frac{4\pi}{5}$ radians, (b) 110°. 2. **Formula:** Arc length $s$ is given

1. **Problem Statement:** Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining

1. **State the problem:** We have two vertical parallel lines cut by a transversal. Given angles 30°, 134°, and 110° on the left line, and angles $x^\circ$ and $y^\circ$ on the rig

1. **Problem statement:** We have an isosceles triangle ABC with vertex A and base BC.