📐 geometry

1. **State the problem:** We are given a triangle with one interior angle measuring 65 degrees and its corresponding exterior angle measuring 115 degrees. We need to find the adjac

1. **State the problem:** We are given a triangle with one interior angle measuring 65 degrees and its corresponding exterior angle measuring 115 degrees. We need to find the adjac

1. **State the problem:** We are given a triangle ABC with angles $B = 80^\circ$ and $C = 60^\circ$. We need to find the value of angle $A$. 2. **Formula used:** The sum of the int

1. **Problem statement:** In triangle ABC, an exterior angle is given as 110 degrees, and one of the interior opposite angles is 50 degrees. We need to find the other interior oppo

1. **Problem 33:** Find the values of angles $x$ and $y$ in a quadrilateral with angles $118^\circ$, $22^\circ$, $x^\circ$, and $y^\circ$. 2. **Formula:** The sum of interior angle

1. **Problem statement:** We have a square with one vertex at $(1,2)$ and its diagonal lies along the line $$8x - 15y = 0.$$ We need to find the equations of the sides of the squar

1. The problem involves finding areas of common shapes given side lengths and angles. 2. For (a) the triangle with sides $p$ and $q$ and included angle $75^\circ$, use the formula

1. The problem asks for the angles of points $p$ and $q$ in figure 5.8 (a). 2. Since the figure is not provided, I will explain how to find angles $p$ and $q$ generally in a triang

1. **Problem Statement:** Find the angles $p$ and $q$ in Figure 5.8(a), angles $r$ and $s$ in Figure 5.8(b), and angle $t$ in Figure 5.8(c). 2. **Given Information:**

1. Problem 8: Classify triangle XYZ with right angle at Y and sides XY and YZ congruent. - Since XY = YZ, triangle XYZ is isosceles.

1. **Problem a:** Find the side length of a square with perimeter 20 cm. 2. The formula for the perimeter of a square is $$P = 4s$$ where $s$ is the side length.

1. **State the problem:** We have a square with side length 4.5 cm. An equilateral triangle with side length 4.5 cm is cut out from one side of the square, creating a "V" shape ins

1. **Problem 1:** Given triangle PQR with sides $q=12$ cm, $r=16$ cm, and angle $P=54^\circ$, find the third side or other unknowns if needed. 2. **Problem 2:** Given triangle PQR

1. **Problem Statement:** We are solving various problems related to three-figure bearings, which are angles measured clockwise from the North line and always written with three di

1. **Problem Statement:** Solve all 8 questions of Exercise 6.6 on Three-Figure Bearings from the Grade 9 Federal Board Maths book. 2. **Important Note on Bearings:** Bearings are

1. **Problem Statement:** Measure bearings and solve related problems involving bearings and distances between points. 2. **Understanding Bearings:** Bearing is the angle measured

1. **Problem Statement:** Measure the bearings of points B from A using a protractor in given diagrams. 2. **Understanding Bearings:** Bearing is the angle measured clockwise from

1. **Given:** $A=29^\circ$, $B=68^\circ$, $b=27$ mm. Step 1: Find $C$ using the angle sum rule: $$C=180^\circ - A - B = 180^\circ - 29^\circ - 68^\circ = 83^\circ.$$

1. **State the problem:** Given an isosceles trapezoid ROMA, prove that the diagonals $\overline{RM}$ and $\overline{AO}$ are congruent. 2. **Given:** ROMA is an isosceles trapezoi

1. **State the problem:** Prove that in isosceles trapezoid ROMA, the diagonals RM and AO are congruent, i.e., $RM \cong AO$. 2. **Given:** ROMA is an isosceles trapezoid.

1. Problem: Given $m\angle COE = 40^\circ$, find arc $CE$. Formula: The measure of an arc is equal to the measure of its central angle.