📐 geometry

1. **Problem statement:** We are given a triangle with points K, L, M and a point N on segment KM. Angles are marked as follows: \(\angle LKN = y^\circ\), \(\angle LNM = 3y^\circ\)

1. **Stating the problem:** We have two circles:

1. **State the problem:** Calculate the surface area of a prism whose cross-section is an isosceles triangle with a rectangular hole inside and an extension on the right side. 2. *

1. Problemet handlar om att hitta vinkeln $v$ som är supplementär till en given vinkel på $142^\circ$. 2. Två vinklar är supplementära om deras summor är $180^\circ$.

1. **Problem statement:** We need to determine if the diagonals AC and BD of quadrilateral ABCD are perpendicular. 2. **Key concept:** Two lines are perpendicular if the product of

1. **State the problem:** Determine if triangle ABC with vertices A(0,4), B(1,2), and C(4,6) is a right triangle. 2. **Recall the rule:** A triangle is right if one angle is 90 deg

1. **State the problem:** Determine if triangle ABC with vertices A(0,4), B(1,2), and C(4,6) is a right triangle. 2. **Recall the formula:** To check if a triangle is right-angled,

1. **Problem Statement:** Given a rectangle ABDF with bottom edge FD = 672 m, and angles $\angle CGL = 53^\circ$ and $\angle HJL = 63^\circ$, we want to analyze the geometry of the

1. **Problem:** Given two similar triangles \(\triangle SRT \sim \triangle CBD\), find the value of \(x\) where sides correspond as follows: \(SR = 11x - 4\), \(RT = 70\), \(CB = 6

1. **State the problem:** We have a 25-foot tall tree and a 10-foot tall fence post. The fence post casts a shadow 22 feet long. We need to find the length of the tree's shadow. 2.

1. **Problem statement:** Calculate the size of angle $NPQ$ in the given polygon with points $N$, $P$, $Q$, and $R$. Given angles are $\angle R = 36^\circ$ and $\angle Q = 107^\cir

1. **State the problem:** We have a square named CUBE with sides CU and UB given as expressions in terms of $x$: $CU = 4x - 5$ and $UB = 2x + 3$. We need to find the measure of $\o

1. **State the problem:** We have a parallelogram TUWV with angles at vertices U and V given as $(x + 158)^\circ$ and $(x + 74)^\circ$ respectively. We need to find the measure of

1. **Stating the problem:** Máme štvouholník ABCD s podmienkami:

1. **Problem Statement:** We have a parallelogram GRPC with points B and E such that triangle GCB and triangle BPE are formed. Given lengths: $GC=375$ ft, $CB=325$ ft, $GB=425$ ft,

1. **State the problem:** We have a rectangle ABCD with AB = 8 and BC = 6. We need to find the lengths of AD, DC, and AC. 2. **Recall properties of a rectangle:** Opposite sides ar

1. **State the problem:** We are given a parallelogram ABCD with side AB = 5 units, side BC = 3 units, and angle at vertex B = 60°. 2. **Recall properties of parallelograms:** Oppo

1. **State the problem:** We need to find the area of a polygon shaped like the number "9" on a grid where each square is 1 cm by 1 cm. The polygon has a square hole inside it, so

1. **State the problem:** We need to find how many 4 feet by 9 feet panels are required to cover the outside perimeter of the structure. 2. **Identify the total perimeter length:**

1. **Stating the problem:** We have a ladder 3.5 m long leaning against a wall.

1. **State the problem:** We need to find the area of the shaded shape WXZY, which is the ring-shaped region between two sectors OWX and OYZ. 2. **Given data:**