📐 geometry

1. **State the problem:** We are given a triangle ABC with angles labeled as follows:

1. **State the problem:** We need to find the measure of angle $\angle ORQ$ given two expressions for angles formed by intersecting lines: $(9x - 4)^\circ$ and $(3x + 40)^\circ$. 2

1. **State the problem:** We are given two angles formed by intersecting lines, with measures $(15x + 11)^\circ$ and $(5x + 69)^\circ$. We need to solve for $x$. 2. **Identify the

1. **Problem statement:** Given two parallel lines \(\overrightarrow{TV}\) and \(\overrightarrow{WY}\), and the angle \(m \angle VUS = 64^\circ\), find the measure of \(m \angle YX

1. **Problem Statement:** We are given two parallel lines \(\overleftrightarrow{JL}\) and \(\overleftrightarrow{MO}\) and several pairs of angles. We need to determine which pair o

1. **Problem Statement:** Given that $\overrightarrow{SU}$ and $\overrightarrow{VX}$ are parallel lines and $m \angle UTR = 139^\circ$, find $m \angle VWY$. 2. **Understanding the

1. The problem asks which pairs of angles are vertical angles given two parallel lines \(\overrightarrow{MO}\) and \(\overrightarrow{PR}\) intersected by a transversal \(\overright

1. **State the problem:** Given that $BA \cong BC$ and $AE \cong DC$, prove that $\triangle BDE$ is isosceles. 2. **Given information:**

1. The problem is to graph a circle. 2. The standard formula for a circle centered at the origin with radius $r$ is:

1. **State the problem:** We have a right triangle with three sides: shorter leg, longer leg, and hypotenuse. The longer leg is 3 cm more than three times the shorter leg.

1. **Problem statement:** Find the total area of each rectangle given the areas of smaller rectangles inside and the lengths of portions of the sides. 2. **Rectangle a:**

1. **State the problem:** Find the area of a rectangle with length 3 feet and width \(\frac{1}{4}\) foot. 2. **Formula:** The area \(A\) of a rectangle is given by \(A = \text{leng

1. The problem asks to find the matching counterclockwise angle for given clockwise angles 175° and 285°. 2. Important rule: A full circle is 360°. Clockwise and counterclockwise a

1. **Problem Statement:** Calculate the volume of water in a pool with given dimensions where water is filled to 9 feet from the top.

1. **Problem Statement:** Determine the image of point $P(-6,4)$ after reflection over the line $y+x=0$, which can be rewritten as $y=-x$.

1. **State the problem:** We need to translate triangle P by the vector $(2, -7)$. This means moving every vertex of the triangle 2 units to the right and 7 units down. 2. **Vertic

1. **Problem:** Find the perimeter of the house in terms of $c$. 2. **Formula:** The perimeter of a polygon is the sum of the lengths of all its sides.

1. **State the problem:** We are given a triangle with two sides measuring 6 mm and 16 mm, and the angle between them is $\theta = 14.4^\circ$. We need to find the area of this tri

1. **State the problem:** Calculate the surface area of a cone with radius $r=7$ cm and height $h=12$ cm. 2. **Formula:** The surface area $A$ of a cone is given by

1. **Problem Statement:** We need to find the image of square JKLM after a 90° counterclockwise rotation around the origin. 2. **Vertices of the original square JKLM:**

1. **State the problem:** We need to find the image of trapezoid EFGH after a 180° counterclockwise rotation around the origin. 2. **Recall the rotation formula:** A 180° rotation