Square Diagonal and Angle Calculation Problem with KM=25

Question

Find the measures below based on the following square diagram. KM=25. Calculate KO=, ∠KLN=, LN=, ∠KNL=, ∠MLN=

Accepted Answer

KO=12.5, ∠KLN=45°, LN=25, ∠KNL=72°, ∠MLN=45°

Answer

Step 1: Identify the figure is a square. In a square, the diagonals are equal, bisect each other, and bisect the interior angles. All interior angles of a square are 90°, and each diagonal splits the square into two isosceles right triangles. Step 2: Calculate KO. Since diagonals of a square bisect each other, KO is half of KM. Given KM=25, so KO = 25÷2 = 12.5. Step 3: Calculate ∠KLN. Diagonals of a square bisect the interior angles. The interior angle ∠KLN is half of the 90° interior angle of the square, so ∠KLN = 90°÷2 = 45°.  Step 4: Calculate LN. Diagonals of a square are equal, so LN = KM = 25. Step 5: Calculate ∠KNL. From the diagram, ∠MNN (marked as 18°) is part of ∠KNM. ∠KNM is 90° (interior angle of square), so ∠KNL = 90° - 18° = 72°.  Step 6: Calculate ∠MLN. Diagonals of a square bisect the interior angles, so ∠MLN is half of the 90° interior angle of the square, so ∠MLN = 90°÷2 = 45°.