📐 geometry

1. **Stating the problem:** We have a quadrilateral ABCD with angles $x^\circ$ at A, $y^\circ$ at D, $38^\circ$ at C, and a right angle (90$^\circ$) at B. Sides AD and DC are equal

1. **Stating the problem:** We are given a polygon with angles labeled as 42°, y°, 40°, 92°, 153°, and x°. We need to find the values of the unknown angles $x$ and $y$. 2. **Formul

1. **Stating the problem:** We have triangle ABC with point D on segment AC such that ADC is a straight line. Given angles: \(\angle A = 77^\circ\), \(\angle C = 35^\circ\), \(\ang

1. **Stating the problem:** We are given two angles: one expressed as $3x^\circ + 50^\circ$ and the other as $285^\circ$. We want to find the value of $x$ if these angles are relat

1. **Stating the problem:** We have a directed polygonal chain with vertices A, B, C, D, E, F, G, H and angles given at certain points: angle at B is $2x^\circ$, angle at C is $162

1. **State the problem:** Find the distance between the points $(4, -4)$ and $(9, -2)$ on the coordinate plane. 2. **Formula used:** The distance $d$ between two points $(x_1, y_1)

1. **State the problem:** Find the distance between the points $(-2, -4)$ and $(4, -6)$ rounding to the nearest tenth. 2. **Formula:** The distance $d$ between two points $(x_1, y_

1. **State the problem:** Identify the transformation that maps points B, C, D forming a "V" shape with vertex at C to points B', C', D' forming an inverted "V" shape with vertex a

1. **State the problem:** We have triangle ABC with vertices A(-3, -2), B(0, 4), and C(4, 1).

1. **State the problem:** We have a right triangle with legs 8 and 32, and hypotenuse $x$. We need to find the value of $x$. 2. **Formula used:** In a right triangle, the Pythagore

1. **State the problem:** Identify all segments parallel to XT in the given 3D figure (a cube-like rectangular prism). 2. **Recall the rule:** Segments are parallel if they lie in

1. **Problem statement:** Given the segment lengths $XL = x + 7$ and $LV = 2x - 5$, find the length of $XY$. 2. **Understanding the problem:** Points $X$, $L$, and $V$ lie on the s

1. **State the problem:** We have an isosceles trapezoid EFGH with sides EG and FH given by expressions $EG = 2s + 93$ and $FH = s + 98$. We need to find the value of $s$. 2. **Rec

1. **State the problem:** We have an isosceles trapezoid GHIJ with $m\angle H = 6z + 28^\circ$ and $m\angle I = 130^\circ$. We need to find the value of $z$. 2. **Recall properties

1. **State the problem:** We are given a trapezoid RTUW with midsegment \( \overline{SV} \). The lengths are given as \( RW = -2p + 65 \), \( SV = p + 50 \), and \( TU = p + 71 \).

1. **State the problem:** We have an isosceles trapezoid DEFG with sides DF and EG given by expressions $DF = 10s + 1$ and $EG = 7s + 40$. We need to find the value of $s$. 2. **Re

1. **State the problem:** We have an isosceles trapezoid EFGH with $m\angle F = c + 49^\circ$ and an adjacent angle measuring $133^\circ$. We need to find the value of $c$. 2. **Re

1. **State the problem:** We are given a trapezoid STVW with midsegment RU. The lengths are given as VW = $3y - 56$, RU = $-2y + 64$, and ST = $y$. We need to find the value of $y$

1. **State the problem:** We are given a trapezoid QRTU with midsegment PS. The lengths are:

1. The problem states that the diameter of a circle is 16 meters, and we need to find the area of the circle rounded to the nearest hundredth. 2. Recall the formula for the area of

1. **State the problem:** We have two intersecting lines forming four angles. One angle is 64°, another angle y is 90°, and we need to find the measure of angle x. 2. **Recall impo