📐 geometry

1. **Problem statement:** Two of the exterior angles of a pentagon are $4x$ and $2x$. The remaining three exterior angles are each $3x$. Find: a. The value of $x$.

1. **Problem statement:** 4.1.1 Complete the statement: In a right-angled triangle, the square of the ________ is equal to the sum of squares of the other two sides.

1. **Problem:** The size of the exterior angle of a regular polygon is 60° less than the interior angle. Find: (a) The size of the interior angle.

1. The problem asks to identify the type of angle shown in the figure. 2. The figure shows an angle less than 90 degrees.

1. **Problem statement:** We have a parallelogram IKLM with sides and angles given:

1. **Problem statement:** Given a parallelogram I, M, K, L with side IM = 6 cm, \(\angle I = 78^\circ\), and \(\angle M = 102^\circ\), find the length of KL and calculate the sizes

1. **Problem statement:** Find the length of side $KL$ and calculate the sizes of angles $\angle K$ and $\angle L$ in the parallelogram $KLM1$ given that $\angle 1 = 78^\circ$, $\a

1. **Problem statement:** We have five vertices of a hexagon plotted at points (2,4), (5,6), (9,6), (11,4), and (9,2) on a grid. The hexagon is equilateral, meaning all sides have

1. **Problem statement:** We have five vertices of a hexagon plotted on a coordinate plane: $A(1,5)$, $B(4,1)$, $C(9,1)$, $D(12,9)$, and $E(4,9)$. We need to find the coordinates o

1. **Problem statement:** We have five vertices of a hexagon plotted on a coordinate grid: (1,5), (4,1), (4,9), (9,1), and (9,9). We need to find the coordinates of the sixth verte

1. **State the problem:** Find the equations of the tangent lines $l_1$ and $l_2$ to the circle given by

1. **State the problem:** We need to find the total surface area of a cuboid with length $6$ cm, width $4$ cm, and height $5$ cm. 2. **Formula for total surface area of a cuboid:**

1. **State the problem:** We need to find the volume of a cylinder with radius $r = 9$ cm and height $h = 20$ cm. 2. **Formula for the volume of a cylinder:**

1. **State the problem:** Find the volume of a triangular prism with a triangular base of base length 7 cm and height 6 cm, and prism length 10 cm. 2. **Formula:** The volume $V$ o

1. **Problem Statement:** We are given a circle with center $O$ and points $P$, $Q$, and $R$ on the circle. The angles at the center $O$ subtended by chords $PR$ and $PQ$ are $60^\

1. **Problem:** If the diagonals of a quadrilateral bisect each other at right angles, then name the quadrilateral. 2. **Formula and rules:** A quadrilateral whose diagonals bisect

1. **Problem:** If the diagonals of a quadrilateral bisect each other at right angles, then name the quadrilateral. 2. **Formula and Rules:**

1. **State the problem:** We need to find the bearing of point D from point C using the protractor diagram. 2. **Understanding bearings:** Bearings are measured clockwise from the

1. **Problem statement:** We need to find the bearing of point A from point B, and the bearing of point B from point A.

1. State the problem: We need to arrange the steps for drawing a bearing of 075° from a point X in the correct order. 2. Understand the concept: A bearing is measured clockwise fro

1. **Problem statement:** In triangle $ABC$, point $D$ lies on $AC$ such that $BD \perp AC$ and $\angle DBC = 77^\circ$. Point $E$ lies on $BC$ such that $\angle CAE = 54^\circ$. W