📐 geometry

1. The problem states that two vertical angles are formed by intersecting lines, with one angle measuring 145° and the opposite angle measuring (2x + 15)°. 2. Vertical angles are a

1. **Stating the problem:** We are given two angles formed by a diagonal line crossing two parallel horizontal lines. The angles are labeled as $(15x - 2)^\circ$ and $(11x + 34)^\c

1. **State the problem:** We are given two angles formed by a transversal intersecting two parallel lines. The angles are labeled as $5x + 6$ degrees and $8x - 39$ degrees. 2. **Id

1. **Problem:** Select all the sets of conditions that will form only one unique triangle. 2. **Understanding the problem:** We need to identify which sets of given conditions guar

1. **State the problem:** We are given two triangles, Triangle A with sides 10, 18, and 15, and Triangle B with sides 6, 4, and 7.2. We need to find the scale factor from figure A

1. **State the problem:** We need to find the total cost to pave all the grey areas in the picnic area. Each grey shape's area must be calculated, then summed, and finally multipli

1. **State the problem:** We are given the area of a square as 36 cm² and need to find the length of one side of the square. 2. **Formula used:** The area $A$ of a square is given

1. **State the problem:** We have a ladder leaning against a building forming a right triangle. The ladder is the hypotenuse of length 35 feet, the building height is one leg of le

1. **State the problem:** We need to find the area of a right trapezoid with bases 12.5 ft and 6 ft, and height 6 ft. 2. **Formula for the area of a trapezoid:**

1. **State the problem:** We need to find the area of an L-shaped composite figure with outer dimensions 14 inches by 14 inches and an inner cutout of 7 inches by 7 inches. 2. **Fo

1. The problem asks to write three proportions involving the geometric mean from the similar right triangles $\triangle GIF$ and $\triangle GHF$. 2. In right triangle similarity wi

1. **State the problem:** We have a right triangle with one leg of length 30, hypotenuse 40, and the other leg divided into two segments: one segment is $x$ (vertical segment), and

1. **State the problem:** We are given two triangles, one larger and one smaller, where the larger triangle is a dilation of the smaller triangle with scale factor $k=2.5$. We need

1. **State the problem:** We are given a triangle with angles measuring 81°, $x$°, and 40°. We need to find the value of $x$. 2. **Recall the triangle angle sum rule:** The sum of

1. **State the problem:** We are given a triangle with three angles: $(4x + 19)^\circ$, $111^\circ$, and $26^\circ$. We need to find the value of $x$. 2. **Recall the triangle angl

1. **Problem:** HIJK undergoes a dilation with a scale factor of 3 centered at the origin. Determine which statements are true. 2. **Understanding dilation:** A dilation centered a

1. **Problem statement:** Given triangle ABCD with point E on side AD such that BE is parallel to DC, and lengths AB = x, BC = 6, AC = 7, CD = 16, find the value of $x$. 2. **Key c

1. **Problem statement:** Find the perimeter of the shaded region in the first shape, which is a quarter circle inside a square with side length 20 cm. 2. **Understanding the shape

1. **State the problem:** We have two similar right triangles \(\triangle ABC \sim \triangle XYZ\). Given sides are \(AC=16\), \(CB=30\), \(AB=34\) in \(\triangle ABC\), and \(YZ=1

1. **Problem Statement:** We are given a circle with a tangent line \(\overrightarrow{GH}\) at point \(H\) and a chord \(\overline{FH}\). The angle between the tangent \(\overright

1. **Problem statement:** Find the measure of angle $\angle LNP$ formed by the intersection of chord $LM$ and secant $PN$ at point $N$ outside the circle. 2. **Relevant theorem:**