📐 geometry

1. **Problem statement:** We are given a sector of a circle with radius $r = 15$ cm and central angle $\theta = 120^\circ$. We want to find the perimeter of this sector. 2. **Formu

1. The problem is to list all points on the x-axis from $-12$ to $12$. 2. Points on the x-axis have coordinates of the form $(x,0)$ where $x$ is the x-coordinate and $0$ is the y-c

1. **Problem Statement:** Given that vectors $\overrightarrow{DF}$ and $\overrightarrow{GI}$ are parallel lines, we want to understand the implications and properties of these para

1. **Stating the problem:** We have two parallel vertical lines \(\overrightarrow{DF}\) and \(\overrightarrow{GI}\). A diagonal line crosses these parallel lines at points \(E\) an

1. **Problem statement:** We have two parallel lines $q$ and $r$ cut by a transversal $s$. The angles formed at the intersections are given as $(7x + 10)^\circ$ on line $q$ and $(3

1. **Problem Statement:** Identify the type of angle pair formed by angles $\angle 3$ and $\angle 6$ given two lines $m$ and $n$ intersected by a transversal line $l$. 2. **Underst

1. The problem is to find the midpoint of a graph, which typically means finding the midpoint of a line segment between two points on the graph. 2. The formula for the midpoint $M$

1. The problem asks: Which angle is complementary to $\angle 5$? 2. Complementary angles are two angles whose measures add up to $90^\circ$.

1. The problem involves identifying relationships between pairs of angles formed by two intersecting lines. 2. When two lines intersect, they form vertical angles which are equal.

1. **State the problem:** We are given a triangle with vertices Miami, Bermuda, and San Juan. The side between Miami and Bermuda is 965 miles, the side between Miami and San Juan i

1. **State the problem:** Determine which of the statements about points $A(0,0)$, $B(a,0)$, and $C(a,b)$ are true. 2. **Recall the definitions:**

1. **State the problem:** We have a large circle with radius $15$ cm and a smaller circle with radius $8$ cm cut out from its center. We need to find the area of the resulting ring

1. The problem is to find the centroid of a triangle given its vertices at points $A(1,2)$, $B(3,7)$, and $C(5,5)$. The centroid is the point where the three medians intersect and

1. **State the problem:** We need to find the measure of angle $\angle QTN$ given two expressions for angles formed by a transversal intersecting two parallel lines. 2. **Identify

1. **State the problem:** We are given two parallel lines cut by a transversal, creating angles \( (9x + 31)^\circ \) at point Q and \( (5x + 47)^\circ \) at point R. We need to fi

1. **State the problem:** We need to find the area of a circle with a diameter of 14 mm. 2. **Recall the formula for the area of a circle:**

1. **State the problem:** We need to calculate the area of a circle with radius $22$ mm. 2. **Formula for the area of a circle:** The area $A$ of a circle is given by the formula:

1. **State the problem:** Megan rode a penny-farthing where the big wheel has radius 36 units and made 9 complete rotations. The small wheel has radius 12 units. We need to find:

1. **State the problem:** Hannah rides a Ferris wheel with radius 22 m that completes 3 full rotations. We need to find the total distance she travels on the ride. 2. **Formula use

1. **State the problem:** We need to find the area of a parallelogram with base length $8$ cm and height $6$ cm. 2. **Formula:** The area $A$ of a parallelogram is given by the for

1. **State the problem:** We need to find the area of a right-angled triangle with base $7$ cm and height $6$ cm. 2. **Formula for the area of a triangle:**