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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1.1 To draw two perpendicular lines intersecting at a point O: Draw a straight horizontal line. Then, draw a straight vertical line that crosses the horizontal line exactly at its midpoint. The point where these two lines intersect is point O. 1.2 To label the angles A, B, C, D formed around the intersection: Starting from the top-right quadrant and moving counter-clockwise, label the angles. • The angle in the top-right quadrant is A. • The angle in the top-left quadrant is B. • The angle in the bottom-left quadrant is C. • The angle in the bottom-right quadrant is D. 1.3 The relationship between the angles: When two lines are perpendicular, they intersect to form four right angles. Therefore, all four angles formed at the intersection are equal to 90^. A = B = C = D = 90^ Additionally, vertically opposite angles are equal ( A = C and B = D), and adjacent angles on a straight line are supplementary (e.g., A + B = 180^). 1.4 Solve for x if one angle is given as 2x + 10^ and a perpendicular angle is 90^. Step 1: Set up the equation. Since the angle is a perpendicular angle, its measure is 90^. 2x + 10^ = 90^ Step 2: Subtract 10^ from both sides of the equation. 2x = 90^ - 10^ 2x = 80^ Step 3: Divide by 2 to solve for x. x = (80^)/(2) x = 40^ The value of x is 40. Send me the next one 📸