📐 geometry

1. **Problem Statement:** Find the slope of the ramps given the side lengths of the triangles. 2. **Formula for slope:** The slope of a ramp is given by the ratio of the vertical r

1. **State the problem:** We have points $A(-3, -4)$, $B(-4, -1)$, $C(-3, 2)$, and $D(1, -2)$.

1. **Problem Statement:** We need to find the coordinates of the images of points $A(-3, -4)$, $B(-4, -1)$, $C(-3, 2)$, and $D(1, -2)$ after reflection about the line $$3x + 2y = 8

1. The problem states that Shape B is a reflection of Shape A across a line. 2. From the graph description, the mirror line is vertical and located at $x = -2$.

1. **State the problem:** We know that shape X' is a translation of shape X by 3 units to the right and 1 unit down.

1. **Problem Statement:** We are given four angle problems involving intersecting lines and reflex angles. We need to find the value of $y$ in each case.

1. **Problem:** Find the unknown angle $y$ when the other angle is $156^\circ$ and both angles form a straight line. 2. **Formula:** Angles on a straight line sum to $180^\circ$.

1. **Problem statement:** Find the unknown angles marked with $y$ in each case. 2. **Step 1:** Understand that angles marked with $y$ are given directly as $24^\circ$, $21^\circ$,

1. **Problem 1:** Find $y$ when three rays meet at a point with angles $156^\circ$, $y$, and the third angle. 2. The sum of angles around a point is always $360^\circ$.

1. Problem: Find the unknown angle $x$ when two adjacent angles on a straight line are $46^\circ$ and $x$. 2. Formula: Adjacent angles on a straight line sum to $180^\circ$.

1. **Problem Statement:** Find the coordinates of the images of points $A(-3, -4)$, $B(-4, -1)$, $C(-3, 2)$, and $D(1, -2)$ reflected about the line $3x + 2y = 8$.

1. **State the problem:** We need to find the coordinates of the points $A(-3,-4)$, $B(-4,-1)$, $C(-3,2)$, and $D(1,-2)$ after reflection about the line $3x + 2y = 8$. 2. **Formula

1. **State the problem:** We want to find the reflection of point $A(2,1)$ about the line $y = -x + 1$. 2. **Rewrite the line in standard form:** The line $y = -x + 1$ can be writt

1. **State the problem:** We need to find the coordinates of the images of points $A(-3,-4)$, $B(-4,-1)$, $C(-3,2)$, and $D(1,-2)$ after reflection across the line $$3x + 2y = 8$$.

1. **State the problem:** We need to find the size of angle $k$ in a triangle where one angle is $83^\circ$ and the triangle is isosceles. 2. **Identify the properties:** In an iso

1. **State the problem:** We have an equilateral triangle with side length $12$ units joined to a half circle on one side. We need to find the perimeter of the combined shape. 2. *

1. **State the problem:** We need to find the measures of angles $U$ and $V$ in rhombus $TUVW$ where $m\angle W = 3c - 30^\circ$ and $m\angle U = 2c + 18^\circ$. 2. **Recall proper

1. **State the problem:** We need to find the distance around the figure, which is the perimeter of a composite shape made of a rectangle and a semicircle. 2. **Identify the parts:

1. **State the problem:** We need to find the measure of angle $G$ in parallelogram $EFGH$ given that $m\angle E = 2c + 9^\circ$ and $m\angle F = c$. 2. **Recall properties of para

1. **State the problem:** We need to find the length of side $GJ$ in parallelogram $GHIJ$ given the expressions for the sides. 2. **Recall properties of parallelograms:** Opposite

1. **State the problem:** We need to find the measure of angle $W$ in rhombus $VWXY$ given the expressions for angles $Y$ and $X$ as $9u+96^\circ$ and $4u+58^\circ$ respectively. 2