📐 geometry

1. **State the problem:** We need to find the value of $x$ and several angle measures given that $AR \cong RO \cong SA$ and the angles $m\angle AMR = 3x + 20$ and $m\angle ONR = x

1. **State the problem:** We are given a circle with center S and points R, A, O, M on the circumference. We know AR \cong RO \cong SA, and the angle measures m\angle AMR = 3x + 20

1. **State the problem:** We have four rays from the origin forming angles. One angle is 24° between the vertical right ray and an upward ray. We need to find the missing angles $x

1. **State the problem:** We need to find the translation that maps Figure Q onto Figure R. 2. **Identify coordinates:** Approximate coordinates of Figure Q vertices are (6,6), (8,

1. **State the problem:** We need to find the perimeter of a sector with a central angle of $70^\circ$ and radius $8$ cm. 2. **Formula for perimeter of a sector:** The perimeter $P

1. **State the problem:** We need to find the combined area of the dark pieces of wood on a cutting board. 2. **Given data:**

1. **Problem:** Given the scale 1.5 inches = 2 feet, find the actual lengths of each room from their drawing lengths. 2. **Formula:** Use the scale factor to convert drawing length

1. The problem asks: Which angle is vertical to $\angle 2$? 2. Vertical angles are pairs of opposite angles made by two intersecting lines. They are equal in measure.

1. **State the problem:** We have a triangle divided into two smaller triangles by a line from one vertex to the opposite side. The left smaller triangle has a top side length of $

1. The problem is to find the length in feet of a line that is separated into two parts by a dotted line. 2. To solve this, we need to know the total length of the line and the pos

1. **State the problem:** We need to find the area of a right triangle with one leg measuring 5.5 ft and the hypotenuse measuring 26 ft. 2. **Recall the formula for the area of a t

1. **State the problem:** We need to find how much more water the cylinder can hold compared to the cone. Both have radius $r=5$ inches and height $h=12$ inches. 2. **Formulas:**

1. **State the problem:** Calculate the volume of a cone-shaped megaphone with height $h=8$ inches and radius $r=9$ inches. 2. **Formula for volume of a cone:**

1. **State the problem:** We need to find the volume of a megaphone shaped like a cone with a height of 8 inches and a base radius of 9 inches. 2. **Formula for the volume of a con

1. **State the problem:** We need to find the volume of a billiard ball which is a sphere with a diameter of 6 centimeters. 2. **Recall the formula for the volume of a sphere:**

1. **State the problem:** We need to find the volume of a cone with height $h=14$ meters and base radius $r=6$ meters. 2. **Formula for the volume of a cone:**

1. **State the problem:** We have two congruent polygons RQOP and XY with given angles and side lengths. We need to find the length of side $QR$ in polygon RQOP. 2. **Understand co

1. **State the problem:** Find the volume of a cylinder with radius $r=0.5$ inches and height $h=4$ inches. 2. **Formula for the volume of a cylinder:**

1. **State the problem:** We need to find the volume of a sphere with radius $r = 4.5$ feet. 2. **Formula for the volume of a sphere:**

1. **State the problem:** We need to find which angles have the same measure as angle $\angle 2$ when two parallel lines $m$ and $n$ are intersected by a transversal $t$. 2. **Reca

1. The problem involves two parallel lines $m$ and $n$ intersected by a transversal $t$, creating eight angles numbered 1 through 8. 2. Important properties when a transversal cros