📐 geometry

1. **Problem:** Find the missing angle $x$ in a quadrilateral with angles $x^\circ$, $78^\circ$, and two right angles ($90^\circ$ each). 2. **Formula:** The sum of interior angles

1. **State the problem:** We need to prove that if three parallel lines cut off equal segments on one transversal, then they cut off equal segments on any other transversal. 2. **G

1. **Énoncé du problème :** Montrer le théorème de Pythagore. 2. **Formule et règles importantes :** Le théorème de Pythagore affirme que dans un triangle rectangle, le carré de la

1. **Énoncé du problème :** Montrer le théorème de Pythagore. 2. **Formule et règles importantes :** Le théorème de Pythagore affirme que dans un triangle rectangle, le carré de la

1. **State the problem:** We have two connected triangles on a horizontal line. The left triangle has a top angle of 65°. The right triangle has a 40° angle at the left base, an un

1. **State the problem:** We have a rectangle with bottom side length 13 and right side length 6. Two semicircles with diameter 6 are removed from the left and right sides. 2. **Id

1. **State the problem:** Given that lines KL and MN are parallel, and lines LM and NO are parallel, find the value of $y$ given the angles $3x^\circ$ at $L$, $96^\circ$ at $M$, an

1. **Problem statement:** Given that lines KL ∥ MN and LM ∥ NO, find the value of $x$ given the angles $3x^\circ$, $96^\circ$, and $2y^\circ$ in the two adjacent triangles KLM and

1. **State the problem:** We have points L, M, and N on a line segment in that order, with M between L and N. 2. **Given:**

1. **State the problem:** We are given a quadrilateral with $AB \parallel DC$, and angles at vertex $A$ labeled as $\angle 1 = 112^\circ$, $\angle 2 = 4x$, and $\angle 3 = 3x + 12$

1. **State the problem:** We are given a quadrilateral with $AB \parallel DC$, and three angles at point $A$: $\angle 1 = 112^\circ$, $\angle 2 = 4x$, and $\angle 3 = 3x + 12$. We

1. **Problem Statement:** Given that lines BA and DC are parallel, identify the type of angle pair formed by \(\angle 1\) and \(\angle 4\), and determine if they are congruent or s

1. **State the problem:** We are given a quadrilateral with $AB \parallel DC$, and three angles: $m\angle 1 = 112^\circ$, $m\angle 2 = 4x$, and $m\angle 3 = 3x + 12$. We need to fi

1. **State the problem:** Given two parallel lines $\ell \parallel m$ cut by a transversal, prove that angles $\angle 3$ and $\angle 5$ are supplementary. 2. **Recall the relevant

1. **State the problem:** We have a linear pair of angles where one angle is 12 degrees less than half the other angle. We need to find both angles. 2. **Recall the property of a l

1. **State the problem:** We need to find the measure of angle $\angle AOB$ given that $m\angle AOB = 4y - 3$ and $m\angle BOC = 6y - 17$. We are told that $\angle AOB$ and $\angle

1. **State the problem:** We need to find the volume of a cylinder with a radius of 8.4 cm and a radius-to-height ratio of 2:6. 2. **Formula for the volume of a cylinder:**

1. The problem asks: Identify the triangle where Pythagoras' Theorem can be applied. 2. Pythagoras' Theorem applies only to right-angled triangles. The formula is:

1. The problem asks: In which triangle can you apply Pythagoras' Theorem? 2. Pythagoras' Theorem applies only to right-angled triangles. It states:

1. The problem asks: In which triangle(s) can you apply Pythagoras' Theorem? 2. Pythagoras' Theorem states that in a right-angled triangle, the square of the hypotenuse ($c$) equal

1. The problem asks which diagram correctly shows Pythagoras' Theorem. 2. Pythagoras' Theorem states that in a right triangle, the square of the hypotenuse ($c$) is equal to the su