📐 geometry

1. **Problem Statement:** We are given a triangle with angles $E=30^\circ$, $F=57^\circ$, and $B=27^\circ$. We need to find the measure of angle $A$. 2. **Recall the Triangle Angle

1. **Problem statement:** We are given a large right triangle with vertices A, B, and I, and inside it smaller angles C = 83°, F = 105°, and E = 37°. We need to find the measure of

1. **State the problem:** We need to find the area of a trapezoid with bases of lengths 38 cm and 18 cm, and legs of 16 cm (height) and 20 cm. 2. **Formula for the area of a trapez

1. **State the problem:** We need to find the area of a parallelogram with a base of 8 cm and a height of 5 cm. 2. **Formula for the area of a parallelogram:**

1. The problem asks why the gradient of the perpendicular bisector of segment AB is -2. 2. First, recall that the gradient (slope) of a line perpendicular to another line is the ne

1. The problem asks to find the value of $x$ in the triangle where the angles are $86^\circ$, $2x$, and $4x$. 2. Recall the Triangle Angle Sum Theorem: The sum of the interior angl

1. **Stating the problem:** We are given a set of angles with relationships involving $x$, $2x$, $y$, and known angles $132^\circ$ and $47^\circ$ in a figure with parallel lines. 2

1. **Problem 1:** In the circle ABCDE, CE is a diameter. Given \(\angle BAC = 36^\circ\), find \(\angle BDE\). 2. **Key fact:** The angle subtended by a diameter in a circle is a r

1. **Stating the problem:** We have a triangle with vertices J (top), M (bottom), and K (right). Given that $JK = MK$, we need to find the length of $JM$. 2. **Understanding the pr

1. **Problem statement:** Given a circle with center O and points A, B, C on the circumference, we know \(\angle ABO = 32^\circ\) and \(\angle BOC = 160^\circ\). We need to find \(

1. **State the problem:** We have a right triangle where one leg is 4 m less than the hypotenuse, and the other leg is 2 m less than the hypotenuse. We need to find the length of t

1. **State the problem:** We need to find the volume of a right-angled triangular prism with base sides 23 m and 38 m, and depth 11 m. 2. **Formula for volume of a prism:**

1. **Problem statement:** Calculate the perimeter (omkretsen) of the figure composed of straight lines and quarter circle arcs. Each square side length is 0.5 cm. Round the answer

1. **State the problem:** Find the volume of the right pentagonal prism with base height 11 mm, base width 8 mm, and prism length 15 mm. 2. **Formula:** The volume $V$ of a prism i

1. **Stating the problem:** We are given a right prism with volume 480 cm³. The base ABCD is a quadrilateral where AD is parallel to BC. Given \(\angle CDA = 90^\circ\), \(BC = 4\)

1. **Problem statement:** A cylindrical block of metal with diameter 1 m and height 2 m is melted to form 2000 cubes. Find the length of each side of the cube in cm. 2. **Formula a

1. **Stating the problem:** A cylindrical block of metal with diameter 1 m and height 2 m is melted to form 2000 cubes. We need to find the length of each side of the cube in cm.

1. **Problem statement:** We have a circle with points L, N, Q on the circumference, where LN = NQ, and RA is tangent at L. Given \(\angle MLN = 63^\circ\), we need to explain why

1. **Problem Statement:** We have a circle with center O and points P, Q, L, N on the circumference. Given that LN = NQ and RM is a tangent at L. Angle MLN = 63°.

1. **State the problem:** Find the values of angles a, d, and e in the circle with center O, points L, M, N, R on the circumference, tangent PQ at R, given \(\angle PRL = 48^\circ\

1. **Problem statement:** We have two similar shapes, S and T. Shape S has a perimeter of 12 cm and a height of 4 cm. Shape T has a height of 40 cm. We need to find the perimeter o