📐 geometry

1. **State the problem:** We have two triangles, a large triangle WZY and a smaller triangle WVX inside it. Given that \(\overline{YZ} \parallel \overline{VX}\), we need to find th

1. **Stating the problem:** We have a triangle with points T, P, and R. Inside the triangle, segment QS is parallel to PT. Given lengths are TS = 42, SR = 21, and RQ = 9. We need t

1. **Problem statement:** We have two triangles WTV and TSV sharing vertex V and side TV. Given WT = 10, ST = 20, TU = 44, and VW \parallel SU, we need to find the length TV. 2. **

1. The problem states that two parallel lines $m$ and $n$ are intersected by a transversal $p$. The angle between $p$ and $m$ is $43^\circ$, and we need to find the value of the an

1. **State the problem:** We have two parallel horizontal lines $m$ and $n$ intersected by a transversal line $p$. An angle of $43^\circ$ is formed at the intersection of $p$ and $

1. **Problem statement:** We need to find the value of $x$ given a geometric figure with angles $\alpha$, $2\alpha$, and $x + \alpha$. 2. **Understanding the problem:** The figure

1. **Problem statement:** Given a triangle with sides $CB=531$ m, $CA=302$ m, and an angle of $49.3^\circ$ at vertex $B$, find the distance $AB$. 2. **Formula used:** We can use th

1. The problem asks for the formula for the volume of a cylinder. 2. The volume $V$ of a cylinder is calculated by multiplying the area of its circular base by its height.

1. **Problem statement:** We are given a triangle with points K, L, M and a point N on segment KM. Angles are marked as follows: \(\angle LKN = y^\circ\), \(\angle LNM = 3y^\circ\)

1. **Stating the problem:** We have two circles:

1. **State the problem:** Calculate the surface area of a prism whose cross-section is an isosceles triangle with a rectangular hole inside and an extension on the right side. 2. *

1. Problemet handlar om att hitta vinkeln $v$ som är supplementär till en given vinkel på $142^\circ$. 2. Två vinklar är supplementära om deras summor är $180^\circ$.

1. **Problem statement:** We need to determine if the diagonals AC and BD of quadrilateral ABCD are perpendicular. 2. **Key concept:** Two lines are perpendicular if the product of

1. **State the problem:** Determine if triangle ABC with vertices A(0,4), B(1,2), and C(4,6) is a right triangle. 2. **Recall the rule:** A triangle is right if one angle is 90 deg

1. **State the problem:** Determine if triangle ABC with vertices A(0,4), B(1,2), and C(4,6) is a right triangle. 2. **Recall the formula:** To check if a triangle is right-angled,

1. **Problem Statement:** Given a rectangle ABDF with bottom edge FD = 672 m, and angles $\angle CGL = 53^\circ$ and $\angle HJL = 63^\circ$, we want to analyze the geometry of the

1. **Problem:** Given two similar triangles \(\triangle SRT \sim \triangle CBD\), find the value of \(x\) where sides correspond as follows: \(SR = 11x - 4\), \(RT = 70\), \(CB = 6

1. **State the problem:** We have a 25-foot tall tree and a 10-foot tall fence post. The fence post casts a shadow 22 feet long. We need to find the length of the tree's shadow. 2.

1. **Problem statement:** Calculate the size of angle $NPQ$ in the given polygon with points $N$, $P$, $Q$, and $R$. Given angles are $\angle R = 36^\circ$ and $\angle Q = 107^\cir

1. **State the problem:** We have a square named CUBE with sides CU and UB given as expressions in terms of $x$: $CU = 4x - 5$ and $UB = 2x + 3$. We need to find the measure of $\o

1. **State the problem:** We have a parallelogram TUWV with angles at vertices U and V given as $(x + 158)^\circ$ and $(x + 74)^\circ$ respectively. We need to find the measure of