📐 geometry

1. The problem states the angles of a quadrilateral are in the ratio 3:4:5:6. We know the sum of angles in any quadrilateral is $360^\circ$. 2. Let the common ratio be $x$. Then th

1. **Stating the problem:** We need to find the length of side $BD$ in a triangle or geometric figure where $BD=15$ is given. 2. **Formula and rules:** Since the problem references

1. The problem states that the length of segment BD is 15, not AB. 2. To solve any related problem, first identify the segments and their lengths clearly.

1. समस्या को समझें: त्रिभुज ABC में AB = BC और \(\angle ABC = 90^\circ\) है, इसका मतलब ABC एक समद्विबाहु समकोण त्रिभुज है।\n\n2. दिया गया है कि AB = 15 इकाई और AD = 17 इकाई। हमें D

1. **Problem statement:** We have a circle with center O and radius $r$ cm. The line PT is tangent to the circle at point P. The angle $\angle POT = \alpha$ radians. The line OT in

1. **Problem Statement:** Complete the missing edge in each Voronoi diagram and find its equation in the form $ax + by + d = 0$.

1. Problem statement: Find the perimeter of triangle ABC whose vertices are A(2,1), B(5,1), and C(5,5). 2. Formula and rules: We use the distance formula to compute each side lengt

1. The problem is to understand the application of the distance formula in coordinate geometry. 2. The distance formula is used to find the distance between two points in a plane.

1. সমস্যাটি হলো: একটি ত্রিভুজের দুটি কোণ $m=60^\circ$ এবং $n=65^\circ$ এবং পরিসীমা 11 সেমি দেওয়া আছে। আমাদের রম্বসের একটি কোণ $m$ ধরে একটি রম্বস অঙ্কন করতে হবে যার পরিসীমা 11 সেমি

1. **State the problem:** Determine which combinations of angle types can form the angles of a triangle. 2. **Recall the triangle angle sum rule:** The sum of the interior angles o

1. **State the problem:** We need to find the size of angle $x$ in a figure where two lines intersect, creating angles of $136^\circ$ and $61^\circ$, and an unknown angle $x$. 2. *

1. **Problem statement:** We have a six-pointed star made up of 6 identical quadrilaterals arranged around a center. Each quadrilateral has an internal angle labeled $x$, and two a

1. **State the problem:** We are given a triangle with angles at vertices A, B, and C labeled as $21x - 1^\circ$, $26x + 6^\circ$, and $11x + 1^\circ$ respectively. We need to find

1. **State the problem:** We need to find the value of $x$ given two connected triangles with angles labeled as follows: first triangle has angles $50^\circ$ and $3x$, second trian

1. **State the problem:** We are given a triangle with two known angles measuring 78° and 66°, and we need to find the measure of the third angle, labeled $x$. 2. **Formula used:**

1. **State the problem:** We are given a triangle with angles 84°, $x + 59$, and $x + 51$, where angle $A$ corresponds to $x + 51$. We need to find the measure of angle $A$. 2. **R

1. **State the problem:** We have a triangle with vertices S, E, and F. There is an exterior angle at vertex D measuring 146°, an interior angle at vertex E measuring 62°, and we n

1. **State the problem:** We have a triangle UST with an exterior angle at vertex S measuring 105°. 2. **Given:** Side US = 12x, side ST = 9x, and the exterior angle at S = 105°.

1. The problem is to understand and apply the formula for the surface area of a prism. 2. The formula given is: $$\text{Surface Area} = 2 \times \text{Area of base} + h \times \tex

1. **Stating the problem:** We need to find the volume of a composite solid made of a cuboid and a pyramid placed on top of it. 2. **Given dimensions:**

1. **State the problem:** We need to find the volume of a triangular-based pyramid (tetrahedron) with a height of 14 cm, a base length of 12 cm, and a segment inside the base trian