📐 geometry

1. **Problem Statement:** Find the ratio between the area of triangle $\triangle ABC$ and $\triangle DEF$ given their side lengths. 2. **Given:**

1. The problem is to find the measure of angle ADC given that angle ADC is 134° and the answer is 88°. 2. This seems to be a misunderstanding or incomplete information because angl

1. **Problem statement:** In circle ABC passing through center O of circle ADC, with ADB a straight line and given \(\angle BDC = 46^\circ\), find \(\angle CBD\). 2. **Key facts an

1. **Problem statement:** We are given a triangle ABC with sides AC = 130, side from C to the unlabeled vertex = 110, and an angle of 38° at the unlabeled vertex adjacent to the si

1. **State the problem:** We have a triangle ABC with side AC = 3, angle A = 35°, and angle C = 85°. We need to find the length of side BC, denoted as $x$. 2. **Use the Law of Sine

1. **Problem statement:** In triangle $\triangle ABC$, angles are given as $\angle A = 30^\circ$, $\angle B = 90^\circ$, and $\angle C = 60^\circ$. Point $X$ lies inside $\triangle

1. **State the problem:** We have a pentagon with five sides and four known angles: 50°, 120°, 80°, and one unknown angle marked with a question mark (?). We need to find the value

1. **Problem statement:** We are given a triangle with side BC = 376, angle A = 98.4°, and angle B = 24.6°. We need to find side AB = x using the Law of Sines. 2. **Law of Sines fo

1. **State the problem:** We are given a triangle ABC with angles $A=98.4^\circ$, $B=24.6^\circ$, and side $c=376$ opposite angle $C$. We need to find side $x$ opposite angle $B$ u

1. **Problem Statement:** Given circle ⊙A with points and angles: $m\angle LAM=42^\circ$, $m\angle HAG=30^\circ$, and $\angle KAH$ is a right angle ($90^\circ$). Find the measures

1. The problem states that ABCD is a rectangle with side lengths AD and AB in the ratio 2:4, and the length DC is given as 16 cm. 2. Since ABCD is a rectangle, opposite sides are e

1. **Problem Statement:** A solid toy is made by surmounting a right circular cone on a hemisphere. Both have the same radius $r = 7$ cm. The height of the cone is $h = 29$ cm. Fin

1. State the problem: You want to find the volume of a sphere given its radius. 2. Use the formula for the volume of a sphere: $$V = \frac{4}{3} \pi r^3$$

1. **State the problem:** We need to find the perimeter of a parallelogram given its side lengths. 2. **Identify the sides:** The parallelogram has two pairs of equal sides. One si

1. **State the problem:** We need to find the perimeter of a parallelogram given its vertices on a grid. 2. **Formula for perimeter of a parallelogram:** The perimeter $P$ is given

1. **Problem statement:** We have a solid cube with side length 10 cm. A pyramid-shaped hole is drilled inside it. The pyramid has a square base of side 5 cm and height 5 cm. We ne

1. **Stating the problem:** We have a right triangle with hypotenuse $d = 5.7$ meters and vertical leg $h = 3$ centimeters. We want to find the length of the horizontal leg. 2. **C

1. **Problem:** In the circle with center O, AOB is a straight line. Find the unknown angle \(\angle ACB\). 2. **Formula and rules:**

1. **Problem statement:** Given a circle with points A, B, C, and D on the circumference, where CD is a diameter, AB is parallel to CD, \(\angle BDC = 70^\circ\), and \(\angle BAC

1. مسئله: شما درخواست یک فرمول ساده و قابل فهم دارید. 2. فرمول پیشنهادی: فرمول مساحت مستطیل که بسیار ساده و کاربردی است:

1. **Problem statement:** We have a heptagon (7-sided polygon) with six interior angles each measuring $x^\circ$ and one interior angle measuring $y^\circ$. Given $y = 126$, find t