📐 geometry

1. **Problem statement:** We need to find the size of angle $x$ at the center $O$ of the circle. 2. **Given information:**

1. **Problem statement:** We are given a circle with center O and points A, B, C, D, and E on the circumference. We know the angle at point D is 148° and need to find the size of a

1. **Problem statement:** We are given a quadrilateral ABCD with right angles at vertices A and D. Inside the quadrilateral, two triangles have areas 10 and 5 respectively. We need

1. **Problem statement:** Find the distance between points A and B in the right triangle where the vertical leg is 49 m, the hypotenuse is 35 m, and the other leg is 26 m. 2. **Ide

1. **State the problem:** We need to find the area of the seating region, which is the ring-shaped sector between two concentric circles with radii 117 m and 23 m, both having a ce

1. The problem asks for the sum of the interior angle measures of a five-sided polygon (pentagon). 2. The formula to find the sum of interior angles of any polygon with $n$ sides i

1. **Problem Statement:** Find the length of the hypotenuse $c$ in each right-angled triangle using the Pythagorean theorem. 2. **Formula:** The Pythagorean theorem states:

1. **Problem Statement:** Find the length of the hypotenuse $c$ in the right-angled triangle with legs 3 and 7, expressing the answer exactly using a surd. 2. **Formula:** Use the

1. **Problem:** Find the length of the hypotenuse $c$ in a right triangle given the legs. 2. **Formula:** Use the Pythagorean theorem:

1. **State the problem:** We need to find the area of each room in the floor plan, the total area to be carpeted, and the total cost of carpeting given the price per square meter.

1. **State the problem:** Calculate the total carpet area of the house using the given floor plan dimensions and then find the total carpet cost at 128.00 per square meter. 2. **Id

1. The problem asks if the triangles in question 11 are similar and if yes, how. 2. To determine similarity of triangles, we use the criteria:

1. **State the problem:** We have a rectangular prism with dimensions length $7$ cm, width $4$ cm, and height $4$ cm. A triangular pyramid (a tetrahedron) with vertical height $2$

1. **Stating the problem:** We have a right triangle with one angle of 45°. The side opposite the 45° angle is $3\sqrt{2}$, the hypotenuse is $x$, and the base is $y$.

1. **State the problem:** Given a right triangle ABC with right angle at C, and segment CE perpendicular to AB, creating two right triangles BEC (with angle B = 60°) and CEA (with

1. **State the problem:** We have a right triangle with one angle of 45°, the side adjacent to this angle is 10, the side opposite is $x$, and the hypotenuse is $y$. We need to fin

1. **State the problem:** We have a right triangle with a 60° angle, the side opposite this angle is 12, the adjacent side is $x$, and the hypotenuse is $y$. We need to find $x$ an

1. The problem asks to identify the relationship between angles 1 and 7 formed by two parallel lines $a$ and $b$ cut by a transversal $h$. 2. Important definitions:

1. **State the problem:** We are given two parallel lines $m$ and $n$ cut by a transversal $t$. Angle 7 measures $75^\circ$. We need to find which angle among 3, 5, 2, and 6 is NOT

1. **State the problem:** We have three parallel lines intersected by two transversals, creating segments with lengths 27, 15, 20, and a missing length $x$ on the bottom horizontal

1. **State the problem:** We need to find the area of a right-angled triangle with a base of 9 meters and a height of 8 meters. 2. **Formula:** The area $A$ of a triangle is given