📐 geometry

1. **Problem:** Classify the angle pair \(\angle 3\) and \(\angle 5\) formed by two parallel lines and a transversal, and determine if they are congruent or supplementary. 2. **For

1. The problem asks for the measure of each interior angle of a regular polygon with 10 sides (a regular decagon). 2. The formula to find the measure of each interior angle of a re

1. The problem asks for the measure of each interior angle of a regular polygon with 12 sides. 2. The formula to find the measure of each interior angle of a regular polygon is:

1. The problem asks which pairs of angles can be adjacent angles. 2. Adjacent angles share a common side and vertex, and their measures add up to less than or equal to 180° because

1. **State the problem:** A student claims that the sum of the measures of a pair of adjacent angles must equal 180°. 2. **Recall definitions:** Adjacent angles share a common vert

1. **State the problem:** We need to find the values of angles $x$, $y$, and $z$ in a parallelogram with given angles and $x=75^\circ$. 2. **Recall properties of parallelograms:**

1. **State the problem:** We have a rhombus W T U V with diagonals intersecting at point X. Given UV = 8 and WX = 5, find the missing measures. 2. **Recall properties of a rhombus:

1. **State the problem:** We need to find the values of $x$, $y$, and $z$ in a parallelogram with given angles: 2°, $x$°, 121°, 31°, 74°, and $y$°. 2. **Recall properties of parall

1. **State the problem:** Find the distance between points $R(-10, -3)$ and $S(-10, -8)$. 2. **Formula used:** The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is give

1. The problem asks for the distance between points U(-9, 5) and V(-9, -8). 2. Since both points have the same x-coordinate, the distance is the vertical distance between their y-c

1. **State the problem:** Given $m<6 = 8x - 3$ and $m<7 = 15x - 1$, find the measures of angles 6 and 7. 2. **Identify the relationship between angles 6 and 7:** Since lines $r$ an

1. **State the problem:** We are given two expressions for angles: $m<7 = 15x - 1$ and $m<8 = 8x - 3$. We need to find the measures of angles 1, 2, and 3. 2. **Analyze the diagram

1. **State the problem:** We have a laptop screen with a diagonal length of 15.6 inches and a height of 7.8 inches. We need to find the width of the screen.

1. **Problem:** Find $m\angle 1$ if $\angle 1$ and $\angle 2$ are vertical angles and $m\angle 2 = 112^\circ$. 2. **Formula and rule:** Vertical angles are congruent, so $m\angle 1

1. **State the problem:** We have points $A(0,135)$ and $C(110,80)$, and point $P$ lies on segment $AC$ dividing it in the ratio $4:7$. Line $AC$ is perpendicular to line $PB$. We

1. **State the problem:** We are given a right triangle with legs 6 cm and 10 cm, and we want to find the hypotenuse $x$ using the Pythagorean theorem. 2. **Formula:** The Pythagor

1. **Problem:** Points B, D, and E lie on a circle. ABC is the tangent to the circle at B. Find the size of angle EDB. 2. **Formula and rules:** The angle between a tangent and a c

1. **Stating the problem:** We are given several angle relationships involving expressions with $x$ and specific angle measures. We need to find the value of $x$ in the first probl

1. **Stating the problem:** We are given multiple geometric figures with angles and side lengths expressed in terms of $x$. We need to find the value of $x$ using the given angle r

1. **State the problem:** We have rectangle ABCD with points A(3,5), midpoint M(1,5) of AB, and midpoint N(-1,-1) of BC. We need to find coordinates of point D. 2. **Recall propert

1. **Problem statement:** Given parallelogram ABCD with points A(-11, 21), B(-14, 28), and C(6, 24), find the coordinates of point D. 2. **Formula and properties:** In a parallelog