📐 geometry

1. **Stating the problem:** We have a triangle with two angles given as 46° each at the top vertices, and we need to find the value of angle $b$ at the bottom vertex. 2. **Recall t

1. **State the problem:** We have two similar trapezoids DEFG (original) and JKLM (new). The top base of DEFG is 40 m, and the corresponding top base of JKLM is 8 m. The left side

1. **Stating the problem:** We are given that \(\angle G = 65^\circ\) and need to find the measure of \(\angle H\). The problem likely involves angles in a geometric figure where \

1. The problem states that the triangle has angles 35\degree, 120\degree, and x\degree, and we need to find the value of x. 2. The sum of the interior angles of any triangle is alw

1. **State the problem:** We need to find the surface area of a rectangular prism with dimensions 2.3 yd (height), 9.5 yd (length), and 1.7 yd (width). 2. **Formula for surface are

1. The problem is to find the value of the angle $x$ in a triangle where the other two angles are $120^\circ$ and $35^\circ$. 2. The key formula to use is the Triangle Angle Sum Th

1. **State the problem:** Find the volume of the L-shaped solid figure composed of two rectangular prisms. 2. **Identify the dimensions:**

1. **State the problem:** We need to find the volume of a rectangular prism made up of unit cubes. The prism has dimensions 3 cubes wide, 4 cubes tall, and 3 cubes deep, with each

1. **Problem statement:** In triangles \(\triangle JLK\) and \(\triangle DEF\), given \(JK = 5\), \(m\angle JKL = 60^\circ\), \(DE = 2x - 3y\), \(m\angle DEF = x + y\), and \(KL =

1. **Problem 18:** Classify the polygon with vertices $S(7, 2)$, $T(1, 2)$, $U(3, -3)$, and $V(5, -3)$ and find its area. 2. **Step 1: Identify the polygon type.**

1. **State the problem:** We have two intersecting lines at point E, creating angles (5x)° and 65° that are opposite each other. 2. **Identify the relationship:** Vertical angles f

1. **Problem Statement:** We have points $A=(0,1)$, $B=(0,0)$, and $C=(1,0)$ in $\mathbb{R}^2$. An isometry $f$ maps these points to new locations in three scenarios. We want to de

1. **State the problem:** Find the value of $x$ in a triangle with angles $60^\circ$, $50^\circ$, and $x$. 2. **Formula:** The sum of angles in any triangle is always $180^\circ$.

1. **State the problem:** We have triangle ABC with AB = AC = 15 cm, CP perpendicular to AB, and CP = 9 cm. We need to find the shaded area formed by the arc centered at B passing

1. **Problem Statement:** (i) Show that the combination of reflections in two parallel lines, distance $\frac{d}{2}$ apart, results in a translation through distance $d$ perpendicu

1. **Problem Statement:** Find the intersection points of the circles given by the equations $$x^2 + y^2 = 1$$ and $$(x-1)^2 + (y-2)^2 = 4$$. 2. **Step 1: Write down the equations

1. The problem asks to identify which transformation of triangle $\triangle ABC$ is a rotation of $30^\circ$ about point $P$. 2. A rotation transformation involves turning a figure

1. **State the problem:** We need to find the weight of 5 washers. Each washer is a cylindrical ring with an inner diameter of $\frac{1}{4}$ inch, outer diameter of $\frac{3}{4}$ i

1. **State the problem:** We are given a circle with a chord and three angles: an outside angle labeled $74^\circ$, an inside angle adjacent to the chord labeled $81^\circ$, and an

1. **State the problem:** We need to find the image of triangle \(\triangle STU\) after a dilation centered at the origin with a scale factor of \(\frac{1}{4}\). 2. **Recall the di

1. The problem asks for the sum of the interior angles of a polygon with seven sides, called a heptagon. 2. The formula to find the sum of interior angles of any polygon is: