📐 geometry

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

1. **Problem:** Calculate the area of a right triangle with base 30 cm and height 16 cm. Formula: Area = \frac{1}{2} \times \text{base} \times \text{height}

1. **State the problem:** We need to find the volume of a rectangular-based pyramid with base length 8 cm, base width 5 cm, and height 27 cm. 2. **Formula for volume of a pyramid:*

1. **State the problem:** We need to find the volume of a rectangular-based pyramid with height $27$ cm, base length $5$ cm, and base width $8$ cm. 2. **Formula:** The volume $V$ o

1. **State the problem:** We need to find the radius of a cylinder given its height and volume. 2. **Recall the formula for the volume of a cylinder:**

1. **Stating the problem:** We want to calculate the surface area of a prism. 2. **Formula and explanation:** The surface area $SA$ of a prism is the sum of the areas of all its fa

1. **State the problem:** We have a mobile login screen layout composed of geometric shapes with given vertices. We need to apply two transformations: a translation 2 units right a

1. Let's start by understanding the problem: we want to find the surface area of 3-dimensional shapes. 2. Surface area is the total area of all the outer surfaces of a 3D object.

1. The problem is to find the value of angle $x$ in a triangle where the angles are $x$, $2x$, and $y=38^\circ$. 2. Recall the triangle angle sum rule: the sum of interior angles i

1. The problem is to find the value of angle $x$ in a triangle where one angle is $y=38^\circ$, another angle is $2x$, and the third angle is $x$.\n\n2. Recall the triangle angle s