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.
ScanSolve AI Answer
let's solve this geometry problem. Starting Blocks First, we'll add up the angles inside each triangle: Triangle 1 (Top Left): 90^ + 45^ + 45^ = 180^ The sum of angles is 180^. Triangle 2 (Top Right): 60^ + 60^ + 60^ = 180^ The sum of angles is 180^. Triangle 3 (Bottom Left): 110^ + 50^ + 20^ = 180^ The sum of angles is 180^. What do you notice? I notice that the sum of the interior angles of every triangle is always 180^. Fill in the size of each angle in the triangles below. Triangle ABC: Step 1: Identify the type of triangle. The tick marks on sides AB and AC indicate that ABC is an isosceles triangle, meaning sides AB and AC are equal. In an isosceles triangle, the angles opposite the equal sides are also equal. Therefore, C = B. Step 2: Determine C. Given B = 30^. So, C = 30^. Step 3: Determine A. The sum of angles in a triangle is 180^. A + B + C = 180^ A + 30^ + 30^ = 180^ A + 60^ = 180^ A = 180^ - 60^ A = 120^ The angles are: A = 120^, B = 30^, C = 30^. Triangle PQR: Step 1: Determine R. The sum of angles in a triangle is 180^. P + Q + R = 180^ Given P = 70^ and Q = 40^. 70^ + 40^ + R = 180^ 110^ + R = 180^ R = 180^ - 110^ R = 70^ The angles are: P = 70^, Q = 40^, R = 70^. Drop the next question.