📐 geometry

1. The problem asks to find the size of angle $x$ given two adjacent angles on a straight line: $50^\circ$ and $35^\circ$. 2. Important rule: Angles on a straight line add up to $1

1. **State the problem:** We need to find the size of angle $n$ given that it and a $52^\circ$ angle form a straight line. 2. **Recall the rule:** Angles on a straight line add up

1. **State the problem:** We have a right triangle with vertices Indianapolis, Dayton, and Lima. The side between Indianapolis and Dayton is 165, the hypotenuse between Indianapoli

1. **State the problem:** We want to find how much closer it is to travel directly from Aurora to Clifton than going from Aurora to Clifton through Burlington. 2. **Identify the tr

1. **State the problem:** We need to find the size of angle $x$ in the given triangle. 2. **Recall the rule:** The sum of the interior angles in any triangle is always $180^\circ$.

1. The problem asks for the value of $x$ such that quadrilateral ABCD is a parallelogram. 2. In a parallelogram, opposite sides are equal in length.

1. **Problem statement:** Given trapezoid-like figure with $TU \parallel VX$, and lengths $UV=15$, $TW=12$, and $TU=25$, find the length $WX$. 2. **Key concept:** When two lines ar

1. **State the problem:** We have a square with side length 4 m, and four quarter circles are drawn inside it, each with radius 4 m, centered at each corner of the square. We need

1. The problem asks for the area of a shape, but the shape and its dimensions are not specified. 2. To find the area, we need to know the type of shape (e.g., rectangle, triangle,

1. **Stating the problem:** We have an orange "X" shaped polygon with given dimensions: vertical height 120 cm, horizontal width 100 cm, inner vertical gap 60 cm, top horizontal in

1. **State the problem:** Given that $PS \perp QR$ and $\triangle PQT \cong \triangle SRT$, prove that quadrilateral $PQSR$ is a rhombus. 2. **Recall definitions and properties:**

1. **Problem 5a:** Verify if point P(-7, -6) lies on the circle with equation $$x^2 + 18x + y^2 - 2y + 29 = 0$$. 2. Substitute $$x = -7$$ and $$y = -6$$ into the circle equation:

1. **State the problem:** We need to find the size of angle $m$ in a quadrilateral where three angles are given: $67^\circ$, $86^\circ$, and a right angle $90^\circ$.\n\n2. **Recal

1. **State the problem:** We need to find the size of angle $p$ in a triangle positioned between two parallel lines, given angles of $109^\circ$ and $125^\circ$ at specific points.

1. **State the problem:** We need to find the value of $a$ in rhombus FGHI where angle $I = a + 56^\circ$ and angle $G = 8a$.\n\n2. **Recall properties of a rhombus:** Opposite ang

1. **State the problem:** We need to find the value of $p$ in parallelogram UVWX where side $UV = 2p$ and side $WX = p + 12$. 2. **Recall the property of parallelograms:** Opposite

1. Problem: Find the missing angle $x$ in a triangle with angles 55°, 50°, and $x$°. 2. Formula: The sum of angles in a triangle is always 180°.

1. **State the problem:** We are given the coordinates of the center of a square at $C(12,7)$ and one vertex at $V(15,10)$. We need to find the area of the square. 2. **Formula and

1. **State the problem:** We are given a rectangle DEFG with center C at coordinates $C(7,9)$ and one vertex $E(20,26)$. We need to find the coordinates of vertex $G$. 2. **Recall

1. **Problem statement:** We have a circle with center $O$ and points $A$ and $B$ on the circle. The chord $AB$ is extended through $B$ to $C$ such that $|BC|$ equals the radius $r

1. Let's clarify what a reflex angle is. A reflex angle is an angle greater than 180 degrees but less than 360 degrees. 2. If you have an angle and you are told it is reflex, it me