📐 geometry

1. **Problem statement:** We are given a protractor image with points A, B, C, and D. Angle ABC is 128° and segment AD is a straight horizontal line along the 0°-180° base of the p

1. **State the problem:** We have a triangle with three angles labeled $a$, $a - 31^\circ$, and $a - 43^\circ$. We need to find the value of $a$. 2. **Recall the triangle angle sum

1. **Nyatakan masalah:** Diberi sektor AOB dengan pusat O, sudut tirus $\theta$ radian, panjang jejari $j$ cm, perimeter sektor 12 cm, dan luas sektor 5 cm². 2. **Formula penting:*

1. **Problem statement:** Given triangle ABC with vertices A(-3,7), B(-8,2), and C(4,6), and point D(-2,k) as the midpoint of BC, we need to: 3.1 Determine the gradient of BC.

1. نبدأ ببيان المسألة: لدينا مثلث ABC بأضلاع $AC=6$ سم، $AB=7$ سم، و$BC=5$ سم. 2. النقطة E هي نقطة على المستقيم AB بالنسبة للنقطة B، والنقطة F هي نقطة على المستقيم AC بالنسبة للنقط

1. **Problem Statement:** Find the value of $x$ in the circle with center $O$ where an angle of $35^\circ$ and an unknown angle $x^\circ$ are given on the circumference.

1. **Problem statement:** In triangle ABC, point D lies on segment AC such that |AD| = |DC|. Given \(\angle DBC = 15^\circ\) and \(\angle ACB = 30^\circ\), find \(\angle ABC\). 2.

1. **Problem statement:** Find the value of $x$ in the first figure where a triangle inside a circle with center $O$ has angles $30^\circ$, $70^\circ$, and $x^\circ$. 2. **Formula

1. **Problem statement:** We have four concentric circles centered at point $M$ with points $N, P, R, S, T, U, V, Y$ on the circles. The segments $|MN| = |NP| = |PR| = |RS|$ are eq

1. **State the problem:** We need to find the volume of a pentagonal prism with a height of 13 cm, each side of the pentagonal base measuring 13 cm, and the apothem (distance from

1. **State the problem:** We need to find the height $H$ of the building given a right triangle formed by the building, the ground, and the lamp. 2. **Identify the known values:**

1. The problem involves understanding a geometric figure where AC and BD are not straight lines, and tangents are involved. 2. Since the answer is given as 55, we need to verify or

1. **Stating the problem:** Given that \(\angle AOB = 125^\circ\), find the measure of \(\angle COD\) in the figure where points A, B, C, D, and O form a pentagon with a circle cen

1. **Problem Statement:** We have two roads: the first road (I. road) is horizontal, and the second road (II. road) is diagonal. Point A lies on the first road, and point B lies on

1. **Problem statement:** We need to find the perimeter of a sector of a circle with radius $10.5$ cm and central angle $\frac{2\pi}{3}$. Given $\pi = \frac{22}{7}$. 2. **Formula f

1. **Problem Statement:** Find the maximum number of hemispheres that can be scooped from a cube. 2. **Understanding the problem:** We want to fit hemispheres inside a cube such th

1. **Problem statement:** From one face of a wooden cube with side length 14 cm, hemispheres of diameter 1.4 cm are scooped out. We need to find the maximum number of hemispheres t

1. **Problem statement:** We have a solid right circular cylinder with height $12$ cm and base radius $5$ cm. A right circular cone with the same height and base radius is removed

1. The problem involves identifying and understanding points on the Cartesian plane, including their coordinates and quadrant positions. 2. The Cartesian plane consists of two perp

1. **Problem Statement:** Given parallelogram ABCD, point P lies on AD such that $AP=\frac{1}{3}AD$, and point Q lies on BC such that $CQ=\frac{1}{3}BC$. We need to analyze or solv

1. **Problem statement:** We have a quadrilateral ABCD with AB \parallel DC and BC \parallel AD. Given angles: \angle B = 121^\circ, \angle A = 40^\circ + z^\circ, \angle C = y^\ci