📐 geometry

1. **Problem statement:** (a) Find the central angle $x$ in a regular octagon.

1. **State the problem:** (a) Find the number of sides of a regular polygon if each exterior angle is 15°.

1. **Problem 1: Find the fifth angle of a pentagon given four angles: 97°, 114°, 127°, and 84°.** 2. The sum of interior angles of a polygon with $n$ sides is given by the formula:

1. **Problem statement:** We have a regular pentagon (5-sided polygon) with center O. We need to find the values of angles $x$ and $y$ shown near one vertex. 2. **Formula for inter

1. **Problem statement:** The radius $r$ of a closed cylinder is equal to its height $h$. We need to find the percentage increase in the total surface area when the height increase

1. **State the problem:** We need to find the approximate increase in the volume of a cylinder when its radius increases from 4 cm to 4.20 cm, given the height is 10 cm. 2. **Formu

1. **Problem statement:** We need to find the dimensions (radius $r$ and height $h$) of a closed right circular cylinder that holds a volume of 1 litre (1000 cubic centimeters) and

1. **Problem Statement:** We have a vertical line segment between points $(6,6)$ and $(6,9)$ on the Cartesian plane. We want to find the image of this segment after a dilation cent

1. 問題陳述： 如圖，梯形 ABCD 外切於圓 O，且 AB = CD，AD = 3，BC = 5，求灰色部分的面積。

1. The problem involves analyzing two trapezoids, Figure A and Figure B, positioned on a coordinate grid. 2. We want to find the area of each trapezoid using the trapezoid area for

1. The problem asks which postulate proves that triangles △ABE and △CDE are congruent based on the given information. 2. The postulates for triangle congruence include:

1. **Problem Statement:** We are given two triangles, \(\triangle JKL\) and \(\triangle OMN\), with the information that side \(JK \cong OM\), angle \(K \cong M\), and a third pair

1. The problem asks which postulate proves that the triangles are congruent given an isosceles triangle ABC with CD perpendicular to AB, and AC = BC. 2. Important information: AC =

1. **State the problem:** We have two congruent triangles \(\triangle RWS \cong \triangle TUV\). We need to find the values of \(x\) and \(y\) given the angles and sides. 2. **Iden

1. **Problem Statement:** Determine which congruency statement is correct among the given options for triangles $\triangle ABC$ and $\triangle DEC$. 2. **Given Information:**

1. **Problem Statement:** Given a circle with center O and arcs AB = 60°, BC = 40°, and DE = 30°, find the measures of angles labeled 1 through 11 based on the given arcs and chord

1. The problem involves understanding the properties of a right triangle with a hypotenuse of length $\sqrt{3}$.\n\n2. In a right triangle, the hypotenuse is the longest side, oppo

1. The problem is to apply the Pythagorean theorem to triangle ABC, which is a right triangle. 2. The Pythagorean theorem states that in a right triangle, the square of the hypoten

1. The problem states that there isn't a right-angled triangle between points A, B, and C. 2. To verify if a triangle is right-angled, we use the Pythagorean theorem: $$a^2 + b^2 =

1. **State the problem:** We need to find the equation of a circle given its center $C$ and radius $r$. 2. **Recall the formula for a circle's equation:** The standard form is $$ (

1. **State the problem:** Lucas and Neal walk on two circular paths given by the equations: