📐 geometry

1. **Problem Statement:** Given angles a, b, c, d, e with some known values and a statement about angles b and f, find the missing angles and verify Theo's claim.

1. **Stating the problem:** We have a triangle ABC with sides $AB=3.6$ cm and $AC=4.3$ cm. Points D and E are defined such that $\vec{AD} = 2\vec{AB}$ and $\vec{DE} = 3\vec{BC}$. W

1. **State the problem:** We have a cylinder with circular faces each having a circumference of 76 mm. The distance from the center of one circular face to the edge of the other ci

1. **Problem statement:** We have a square-based pyramid with a base side length of 6 cm and triangular faces with slant height 11 cm. We need to find the vertical height of the py

1. **Problem Statement:** Determine if triangle $\triangle NMB$ is semi-equilateral given the angles and side lengths in $\triangle ANB$ and the geometric relationships described.

1. **Problem statement:** Given a semicircle with diameter $AB$ and center $O$ where $OB=4$ cm, point $N$ lies on the semicircle such that $\angle NBA=30^\circ$. Tangents at $N$ an

1. **Problem Statement:** Femi travels 10 km South, then turns 90° clockwise and travels 5 km, then turns 90° anti-clockwise and travels another 5 km. We need to find the direction

1. **Problem Statement:** Buchi starts from home and moves 8 km south, then 5 km east, then 3.5 km north, and finally 5 km west. We need to find the direction in which she is movin

1. The problem states that a boy initially faces south. 2. He first turns 45° clockwise. Since clockwise from south moves towards west, the new direction is south-west (SW).

1. **Problem statement:** We are given a geometric figure with angles 99°, 34°, 35°, and an unknown angle $x$. We need to find the value of $x$. 2. **Understanding the figure:** Th

1. **State the problem:** We have a circle with center $O$ and points $A$ and $C$ on the circumference. Lines $AB$ and $BC$ are tangents to the circle at points $A$ and $C$ respect

1. **Problem statement:** We need to find the diameter of a bolt circle given the bolt distance (chord length) of 7 cm and the angle between the diameter and the bolt distance line

1. Problem: Find the size of the lettered angles a°, b°, c°, d°, e°, f°, g°, h°, i°, j°, k°, l°, m° given the relationships in the figure. 2. Formula and rules:

1. **State the problem:** We need to find the surface area of the lower rectangular prism given its dimensions and the total surface area of the stacked prisms. 2. **Given data:**

1. **State the problem:** We need to find the surface area of the lower rectangular prism only, excluding the area where it touches the upper prism. 2. **Given dimensions:**

1. **State the problem:** We need to find the surface area of the lower prism and the total surface area of the combined prisms, excluding the areas where they touch. 2. **Given da

1. **Problem statement:** Two parallel lines $m$ and $n$ are intersected by a transversal, creating four angles: $(10x + 5y)^\circ$, $72^\circ$, $80^\circ$, and $(15x + 4y)^\circ$.

1. **Problem Statement:** We need to understand what it means for two rectangles to be similar. 2. **Definition:** Two rectangles are similar if their corresponding side lengths ar

1. **State the problem:** We are given the total surface area (T.S.A) of a cube as 600 m². We need to find the lateral surface area (L.S.A) and the volume of the cube. 2. **Recall

1. **Problem Statement:** Two cuboids each with dimensions 10m (length) × 8m (width) × 5m (height) are joined end to end. We need to find the Lateral Surface Area (LSA), Total Surf

1. **Problem statement:** Two cubes each with volume 12.5 cm³ are joined end to end. We need to find the Lateral Surface Area (LSA), Total Surface Area (TSA), and volume of the res