📐 geometry

1. **Problem Statement:** Given two parallel lines $m \parallel n$ and a transversal $t$, find the value of $x$ given the angles $(x - 30)^\circ$ and $(3x - 10)^\circ$ at the inter

1. **Problem statement:** We are given a square ABCD with sides labeled as follows: AB = 18, BC = 3(y - 1), CD = 9x, and AD = 2y + 4. We need to find the values of $x$ and $y$. 2.

1. **State the problem:** We have a parallelogram ABCD with sides labeled as follows: - Side CB = $2y - 4$

1. **Énoncé du problème :** Soit ABCD un rectangle avec AB = 5 cm et BC = 2 cm.

1. **Énoncé du problème :** Soit ABCD un rectangle avec $AB=5$ cm et $BC=2$ cm.

1. **Problem Statement:** Calculate the surface area of a right triangular prism with legs of the right triangle base measuring $1.7$ feet and $2$ feet, and the prism length is $4$

1. **Problem Statement:** Calculate the volume of a right triangular prism with legs of the right triangle base measuring $1.7$ feet and $2$ feet, and the prism length is $4$ feet.

1. **Problem statement:** A cruise ship sails north for 50 km, then turns east and sails another 50 km. We need to find the exact direct distance from the start to the finish of th

1. **State the problem:** We have a right triangle with vertices M, C, and D, right angle at C. Point B lies on segment CD, and we want to find the length of BC. 2. **Given data:**

1. **Problem statement:** We are given a geometric figure with two parallel horizontal lines and three angles: 100° between the vertical line and the top horizontal line, 45° betwe

1. **Problem Statement:** We have a triangle ABC inscribed in a circle. Points P, Q, and R lie on arcs AB, BC, and AC respectively. We need to prove that $$\angle ARC + \angle CQB

1. **Problem Statement:** We have a triangle ABC inscribed in a circle. Points P, Q, and R lie on arcs AB, BC, and AC respectively. We need to prove that $$\angle ARC + \angle CQB

1. The problem asks to name the adjacent interior angles of the given triangle. 2. Adjacent interior angles in a triangle are pairs of angles that share a common side and vertex in

1. The first question asks: How many sets of exterior angles does a given triangle have? 2. A triangle has exactly 3 exterior angles, one at each vertex, formed by extending one si

1. مسئله: دو مثلث متشابه داریم که نسبت تشابه آنها ۲ است و محیط مثلث کوچکتر ۸ است. اضلاع مثلث بزرگتر به صورت $1$, $2x^2 - 3x$, $x + 3x^2$, و $4 - x$ داده شده‌اند. باید مقدار $x$ را

1. The problem is to find the formula for the perimeter of a shape. 2. The perimeter is the total distance around the boundary of a two-dimensional shape.

1. The problem is to find the formula for the perimeter of a shape. 2. The perimeter is the total distance around the boundary of a two-dimensional shape.

1. **Stating the problem:** We have triangle UVR with points T and S inside it. Given that RT = TU, \(\angle VST = 23^\circ\), and \(\angle RVS = 44^\circ\), we need to find the an

1. The problem is to find the value of the angle $x$ in a triangle where the other two angles are given as $136^\circ$ and $61^\circ$. 2. Recall that the sum of the interior angles

1. **Stating the problem:** We have a triangle with two marked angles: one is 81° and the other is $k$. The triangle has two pairs of equal sides, indicating it is an isosceles tri

1. **Problem Statement:** You have several points each with an attached vector of length $r$, and you want to find the surface defined by the ends of these vectors. 2. **Understand