📐 geometry

1. **Problem Statement:** (a) Find the size of angle $\angle ACB$ in triangle $ABC$ where $BC=AC=7$ cm.

1. The problem asks to find the bearing of Liverpool from London given the bearing of London from Liverpool is 130°. 2. Bearings are measured clockwise from the north direction. Th

1. **Problem Statement:** We have several geometry problems involving triangles and polygons with given side lengths and angles. We will solve for areas, side lengths, and angles s

1. **Problem Statement:** Given a diagram with two parallel lines cut by a transversal, find the unknown angles $x$, $y$, and $z$ using properties of corresponding angles, interior

1. **State the problem:** We need to find the measure of angle $\angle GMK$ given two expressions for angles formed by parallel lines and a transversal. 2. **Identify the angles:**

1. **Problem Statement:** We need to find the measure of angle $\angle GMK$ given two expressions for angles related by parallel lines and a transversal. 2. **Given:**

1. **State the problem:** We are given two angles formed by a transversal intersecting two parallel lines. The angles are \((2x + 122)^\circ\) and \((154 - 2x)^\circ\). We need to

1. **State the problem:** We need to find the measure of angle $\angle MON$ given two algebraic expressions for angles formed by intersecting lines. 2. **Identify the angles:** The

1. **Problem Statement:** We need to find the measure of angle $\angle QWU$ given two angles formed by a transversal crossing two parallel lines: one angle at point $V$ is $(100 -

1. დავიწყოთ 4.1-ით: წრფოს განზომლა ორ წერტილს შორის არის მანძილი, რომელსაც ვთვლით ფორმულით: $$d=\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$

1. **Problem Statement:** We are asked to identify and draw two lines of symmetry for each given shape: a rectangle, an ellipse, a circle with a diagonal line, and a capsule shape.

1. **Problem statement:** We need to find the size of angle $\theta$ in an isosceles triangle where the two equal sides each measure 5.9 cm and the base measures 4.6 cm. The angle

1. **Problem statement:** We need to find the size of the vertex angle $\theta$ in an isosceles triangle where the two equal sides each measure 5.9 cm and the base measures 4.6 cm.

1. **Nyatakan masalah:** Diberi segi tiga OAB dengan titik O(0,0), A(2,-2), B(6,4), dan titik Q(4,1) pada garis AB. Garis OB mempunyai persamaan $y=\frac{2}{3}x$. Titik P terletak

1. **Problem statement:** We have points $X(0,0)$, $Y(7,24)$, and $Z(15,0)$. Point $W$ lies on segment $YZ$ such that $\angle WXZ = 3 \times \angle WXY$. We need to find the coordi

1. **Problem statement:** Given points $X(0,0)$, $Y(7,24)$, and $Z(15,0)$, find the coordinates of point $W$ on line segment $YZ$ such that $\angle WXZ = 3 \times \angle WXY$. 2. *

1. **State the problem:** We have triangle A plotted on the coordinate plane. We need to:

1. **Problem Statement:** Given quadrilateral ABCD with (i) \(\angle DAC = \angle BCA\) and (ii) ABCD is a parallelogram, prove these properties. 2. **Step 1: Isosceles Triangle Pr

1. **Problem Statement:** We are given a regular 10-sided polygon (decagon) labeled ABCDEFGHIJ. Two angles, $x$ at vertex J and $y$ at vertex B, are marked inside the polygon. We n

1. **Stating the problem:** Given triangle ABC with points D on AC and E on AB such that BD = CE and BE = CD, we want to analyze the geometric relationships. 2. **Understanding the

1. **Problem 1:** Find the area of a triangle with two sides 29 m and 98 m, and included angle 132°. 2. **Formula:** Area = $\frac{1}{2}ab\sin(C)$ where $a$ and $b$ are sides, $C$