📐 geometry

1. **Problem statement:** We have a transversal line $t$ crossing two parallel horizontal lines $a$ (upper) and $m$ (lower). The angles at the upper intersection are labeled 1, 2,

1. **State the problem:** We have a transversal line $t$ crossing two horizontal lines $a$ (top) and $m$ (bottom), creating angles at the intersections. Given that angle 7 measures

1. **State the problem:** The diameter of a circle is 2 feet. We need to find the circumference of the circle in terms of $\pi$. 2. **Formula:** The circumference $C$ of a circle i

1. The problem states that a group of students formed a circle with a circumference of about 43.96 feet and a diameter of 14 feet. 2. We want to find the expression that best repre

1. **State the problem:** In circle H, we are given two angles: $m\angle DHG = (11x - 36)^\circ$ and $m\angle GHF = (x + 12)^\circ$. We need to find the measure of arc $DG$.

1. **Problem statement:** Given rectangle WXYZ with $m\angle XZY = 63^\circ$, find $m\angle WYX$ and $m\angle WVZ$. The diagonals WY and XZ intersect at point V. 2. **Recall proper

1. **Problem Statement:** In rectangle ABCD, the measure of angle AEB is given as 84°. We need to find the measures of angles BDC and EBC. 2. **Important Properties:**

1. The problem asks for one additional fact that guarantees a frame with opposite sides congruent is rectangular. 2. A rectangle is a parallelogram with four right angles.

1. The problem asks about the properties of angles and diagonals in a rectangle. 2. In any rectangle, all angles are right angles, meaning each angle measures 90 degrees.

1. **State the problem:** Find the volume and surface area of the given composite triangular prism-like solid with base 4 cm, height 6 cm, and slanted side 4 cm. 2. **Volume formul

1. **State the problem:** We need to find the length of side $x$ in a right triangle where one leg is 6 units and the angle opposite to $x$ is $70^\circ$. 2. **Identify the sides a

1. **Problem statement:** Given a right triangle ABC with right angle at B, side BC = 7, angle \(\beta = 70^\circ\), and angle \(\alpha = 20^\circ\), find the missing sides AB and

1. **State the problem:** We have a wax candle shaped like a square base pyramid with base side length 6 inches and height 7 inches. The wax burns at a rate of 4 cubic inches every

1. **Problem statement:** JK is tangent to the circle at point L. The arc LM measures 114° and the angle formed between the tangent JK and chord LM at point L is given as (21x - 24

1. **State the problem:** In triangle $\triangle DEF$, angle $\angle F$ is a right angle ($90^\circ$). The sides are given as $DF=8$, $FE=15$, and $ED=17$. We need to find the rati

1. **State the problem:** Find the surface area of a rectangular prism with length $8$ ft, height $6$ ft, and depth $2$ ft. 2. **Formula:** The surface area $SA$ of a rectangular p

1. **State the problem:** We are given three angle sum expressions involving angles of triangle ABC and angle CAD. We want to understand and verify these expressions. 2. **Recall t

1. **State the problem:** We need to find the volume of an in-ground swimming pool with a water depth of 3.5 feet and then find the area of the solar cover for the pool. 2. **Analy

1. **State the problem:** We have two pairs of similar polygons. For each pair, we know the scale factor between the smaller and larger polygon and need to find the missing side le

1. **State the problem:** Find the area of a compound figure composed of a tall rectangle with a semicircle on the top-right and a rectangular notch on the right side. 2. **Identif

1. The problem is to find the "omkreds" which is Danish for "perimeter" of a shape. 2. The perimeter of a polygon is the sum of the lengths of all its sides.