This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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You're on a roll — Here are some geometry problems with explanations, followed by the explanations of the terms you asked for. Geometry Problem 1: Angles in a Triangle Problem: A triangle has two interior angles measuring 50^ and 65^. What is the measure of the third interior angle? Step 1: Recall the property of angles in a triangle. The sum of the interior angles in any triangle is always 180^. Step 2: Set up the equation. Let the three angles of the triangle be , , and . We are given = 50^ and = 65^. We need to find . + + = 180^ 50^ + 65^ + = 180^ Step 3: Solve for the unknown angle. First, add the known angles: 115^ + = 180^ Now, subtract 115^ from both sides to find : = 180^ - 115^ = 65^ The measure of the third interior angle is 65^. --- Geometry Problem 2: Area of a Rectangle Problem: A rectangular garden has a length of 12 meters and a width of 7 meters. What is the area of the garden? Step 1: Recall the formula for the area of a rectangle. The area (A) of a rectangle is calculated by multiplying its length (L) by its width (W). A = L × W Step 2: Substitute the given values into the formula. Given L = 12 meters and W = 7 meters. A = 12 m × 7 m Step 3: Calculate the area. A = 84 m^2 The area of the garden is 84 m^2. --- Explanation of Terms: Coast (Coastal) A coast is the land along a sea or ocean. It is the boundary where land meets a large body of water. The term coastal refers to anything related to or situated on a coast, such as coastal towns, coastal erosion, or coastal ecosystems. Savanna zone A savanna zone is a grassland ecosystem characterized by scattered trees that are not dense enough to form a closed canopy. These zones are typically found in tropical or subtropical regions and experience distinct wet and dry seasons. They support a wide variety of wildlife, particularly large grazing animals. Igoso dynasty I could not find historical information about an "Igoso dynasty." It is possible there might be a slight misspelling, or it refers to a very specific local or less documented historical entity. If you have more context or a different spelling, please provide it, and I can try to find more information. What's next? Send 'em!