📐 geometry

1. **State the problem:** We have a triangle with points T, S, Q, and R, S, Q, where angles at T and R are right angles. We want to find the value of $c$ given the angles $5c$ and

1. **State the problem:** We have two triangles with given angles and need to find the unknown angles $x$, $y$, and $z$. 2. **Recall the triangle angle sum rule:** The sum of the i

1. **State the problem:** We have a triangle with angles 70°, 119°, 28°, and two unknown angles labeled $x$ and $y$. We need to find the values of $x$ and $y$, and analyze how chan

1. **State the problem:** We need to find the value of angle $z$ in a geometric sketch where three angles are given: $72^\circ$, $39^\circ$, and $105^\circ$. These angles are part

1. **State the problem:** We have a sector AOB of a circle with center O and radius $3r$ cm.

1. **State the problem:** We are given the circumference of a circle as $4\pi$ inches and need to find its radius $r$ in inches. 2. **Formula used:** The circumference $C$ of a cir

1. **State the problem:** We are given the circumference of a circle as $5\pi$ cm and need to find its diameter in centimeters. 2. **Formula used:** The circumference $C$ of a circ

1. **Problem statement:** Find the length of the unknown side in the first problem (a right triangle with one leg 6 cm and unknown hypotenuse). 2. **Formula used:** In a right tria

1. **State the problem:** Find the surface area of a sphere with radius $r = 12$ cm. 2. **Formula:** The surface area $A$ of a sphere is given by the formula:

1. The problem asks to find the length of side $ST$ in parallelogram $RSTU$. 2. In a parallelogram, opposite sides are equal in length. Therefore, $ST = RU$ and $RS = TU$.

1. **State the problem:** We need to find the measure of angle $\angle Y$ in rhombus $WXYZ$ where $m\angle Y = c$ and $m\angle Z = 2c + 24^\circ$. 2. **Recall properties of a rhomb

1. **State the problem:** We need to find the measure of angle $C$ in rhombus $BCDE$ where $m\angle C = x + 56^\circ$ and $m\angle D = x$.\n\n2. **Recall properties of a rhombus:**

1. **State the problem:** We need to find the length of side $GH$ in parallelogram $EFGH$. 2. **Recall properties of parallelograms:** Opposite sides in a parallelogram are equal i

1. The problem asks to identify specific points or features on your diagram. 2. To help you accurately, I need to know what points or features you want to locate (e.g., intercepts,

1. **State the problem:** We are given triangle WXY with angles $m\angle WXY = 45^\circ$, $m\angle YWX = 90^\circ$, and side $WX = 5$ feet. We need to determine which triangle (a),

1. **Problem statement:** Calculate the area of the shape consisting of a right triangle attached to a semicircle on the left. The semicircle has radius 4 meters, and the triangle

1. **State the problem:** We need to find the measure of angle $\angle FGJ$. 2. **Given information:** The angle between $FG$ and $GH$ is $57^\circ$, and the angle between $GH$ and

1. **State the problem:** We need to find the measure of angle $m\angle TQW$ given that $m\angle ZQY = 67^\circ$ and $m\angle RQX = 67^\circ$.\n\n2. **Analyze the figure:** Point $

1. **State the problem:** We have a kite DEFG with angles \(m\angle DEF = (12x - 16)^\circ\), \(m\angle EFH = (3x - 1)^\circ\), and \(m\angle DGF = 74^\circ\). We need to find \(m\

1. **State the problem:** We have a right triangle with vertices A, B, and C, where angle B is the right angle. The sides are AC = 24, BC = 10, and we want to find $\cos C$ as a fr

1. **State the problem:** We need to find the value of $\tan E$ in the right triangle $EDC$ where $ED=24$, $DC=32$, and hypotenuse $EC=40$. The right angle is at $D$. 2. **Recall t