📐 geometry

1. **State the problem:** We are given two adjacent angles on a straight line, labeled $(-7y + 97)^\circ$ and $(3y + 75)^\circ$, and we need to find the value of $y$. 2. **Use the

1. **State the problem:** We need to find the radius of a circle given its circumference is $45\pi$ centimeters. 2. **Formula used:** The circumference $C$ of a circle is related t

1. **State the problem:** We are given a semicircle with radius $2$ and want to understand its properties. 2. **Formula for a circle:** The equation of a circle centered at the ori

1. **Problem statement:** Find the perimeter and area of a composite figure consisting of a rectangle, a quarter circle on the left, and a semicircle on the right. 2. **Given dimen

1. **State the problem:** Find the diameter of a circle given its area is 415.48 square inches. 2. **Formula used:** The area $A$ of a circle is given by the formula $$A = \pi r^2$

1. **State the problem:** Given triangle $\triangle WXY$ with $m\angle X = 15^\circ$, $m\angle Y = 20^\circ$, and side $WY = 7.5$, find all sides and angles. 2. **Find the missing

1. **Stating the problem:** We are given two triangles, $\triangle XYZ$ and $\triangle RYS$, which are similar, denoted as $\triangle XYZ \sim \triangle RYS$. 2. **Understanding si

1. **Problem:** Find the measure of angle A in triangle ABC where angles are given as $4x + 5$, $5x$, and $6x + 10$. 2. **Formula:** The sum of interior angles in a triangle is alw

1. **State the problem:** We have parallelogram JKLM reflected across the y-axis and then translated down 6 units to form parallelogram QRST. We need to determine which statements

1. The problem statement is unclear as it mentions "no 60 or 8 in these angels" which seems to be a typo or incomplete. 2. If you meant "angles" and are referring to a problem invo

1. The problem states that angles 2 and 3 are each 52 degrees, and we need to understand how to find or verify this. 2. Typically, angles labeled 2 and 3 might be related by geomet

1. **Stating the problem:** We are given a geometric figure with intersecting lines and angles, and we need to find unknown angles based on the given information. 2. **Given angles

1. **State the problem:** We are given a triangle with vertices A, B, and C. The angle at vertex A is given as $2x - 20$ degrees. The sides opposite vertices B and C are labeled wi

1. The problem asks to identify the type of triangle given that sides AB and AC are equal, both labeled with length $x$. 2. In geometry, a triangle with two equal sides is called a

1. **Stating the problem:** We are given two intersecting lines forming a Z shape with angles marked as 100° and 76°, and two angles labeled 1 and 2. We need to find the measures o

1. **State the problem:** We have two right triangles sharing a common horizontal side. The upper triangle has a hypotenuse of length $7\sqrt{3}$ and angles $45^\circ$ and $90^\cir

1. Stating the problem: We have four lines AB (horizontal), MN (diagonal), and PQ (vertical). 2. Given: AB meets MN at B with angle between them $76^\circ$.

1. **State the problem:** We are given a triangle DEF with angles at vertices D, E, and F labeled as $x$, $2x$, and $5x$ respectively. We need to find the measure of angle $D$, whi

1. **State the problem:** We need to find the length of side AC (labeled as $b$) in a right triangle with side BC = 5.0 cm and angle at vertex B = 27°.

1. **State the problem:** We need to find the cost to fill a conical silo with rice. The silo has a height $h=7$ meters and a base radius $r=1.5$ meters. Rice costs 204 per cubic m

1. **State the problem:** We need to find how many truckloads are required to move a pile of sand shaped like a cone. The cone has a height of 9 yards and a base diameter of 10 yar