📐 geometry

1. **Problem Statement:** Identify which angle is complementary to \(\angle 2\) given the angles formed by two intersecting lines. 2. **Recall definitions:**

1. **State the problem:** We need to find the length of the diagonal $AG$ in a cuboid where edges $AB$ and $AD$ meet at a 75° angle, with $AB=23$ cm and $AD=18$ cm. 2. **Understand

1. **State the problem:** Find the angle $\theta$ in triangle A-5 where the legs are 5 and unknown $\theta$, and the hypotenuse is 13.

1. **State the problem:** We need to find the scale factor that takes rectangle Y to rectangle Z. 2. **Identify the dimensions:**

1. The problem is to explain the concept of length between two points $p$ and $q$ in a coordinate system. 2. The length (or distance) between two points $p=(x_1,y_1)$ and $q=(x_2,y

1. **Problem Statement:** Calculate the lengths $p$ and $q$, the perimeter, and the area of an L-shaped plot of land with given segment lengths. Then find the maximum number of ban

1. **Problem statement:** Calculate the area of a square when its diagonal length is given as $1.6 + a$ cm. 2. **Formula used:** The area $A$ of a square with diagonal $d$ is given

1. **Stating the problem:** We need to find the area of the sector ALB of a circle with center L, where AL = 14 cm, angle LAC = 25°, and AC = BC.

1. **Problem Statement:** Given a right triangle ABC with right angle at A, side AB = 4, side AC = 3, and BC is the hypotenuse. Find the measure of the shaded angle (assumed to be

1. **Problem statement:** We have a right triangle with hypotenuse 24 and base 9, and a vertical side labeled $x$. We need to find the length of $x$. 2. **Formula used:** In a righ

1. **State the problem:** We need to find the area of a rectangle with side lengths $5\sqrt{7}$ cm and $2\sqrt{7}$ cm. 2. **Formula for the area of a rectangle:**

1. **Problem statement:** Reflect the point $(4,6)$ across the y-axis and x-axis. 2. **Reflection across the y-axis:**

1. **State the problem:** We have points $X(-5,7)$, $Y(-4,-11)$, and $Z(9,-6)$. They are reflected over the x-axis to points $X'$, $Y'$, and $Z'$.

1. The problem is to find or understand 2 line segments. 2. A line segment is a part of a line bounded by two distinct endpoints.

1. **State the problem:** We need to find the area of the irregular polygon drawn on the grid where each square represents 1 cm by 1 cm. 2. **Calculate the area:** Count the full 1

1. **State the problem:** Ruby has 4 identical right-angled triangles with sides 12 cm, 16 cm, and 20 cm. She arranges them to form a star. We need to find the perimeter of the sta

1. **State the problem:** We have triangle $\triangle ABC$ with sides $a = 15$ cm, $b = 18$ cm, and angle $\angle C = 48^\circ$. We want to find side $AB$ and angle $A$ using both

1. **State the problem:** We have a quadrilateral with four angles: 70°, 76°, 90°, and an unknown angle $r$. We need to find the value of $r$. 2. **Recall the formula:** The sum of

1. **State the problem:** We are given the exterior angles of a convex hexagon as expressions involving $t$: $5t - 38^\circ$, $7t - 43^\circ$, $36^\circ$, $t + 20^\circ$, $6t - 24^

1. **State the problem:** We need to find the number to multiply each distance on the map (in cm) to get the actual distance (in km). 2. **Identify the scale:** The scale given is

1. **State the problem:** We need to find the scale factor to convert map distances to actual distances, and then use it to find the actual distance from Osc's campsite to the gene