Quadrilateral J K L M is shown. A diagonal is drawn from point J to point L. Sides K L and J M are parallel. Sides J K and L M are congruent. The length of J L is 18, the length of J K is 16, and the length of J M is 40. Angle M is 45 degrees. If KM is drawn on this quadrilateral, what will be its length?

KM is 52.55

Step-by-step explanation:

Given that JKLM is a quadrilateral with a diagonal drawn from J to L, we have;

Sides KL is parallel to side JM

Side JK is congruent to side LM

Therefore, sides JK and LM are parallel being the equal distances between two parallel lines

JL = 18, JK = 16, therefore, LM = 16, JM = 40 therefore, KL = 40 (equal distances between parallel lines JK and LM)

∠M = 45° ∴ ∠L = 180° - 45° = 135° (sum of adjacent interior angles of a parallelogram)

By cosine rule, we have;

KM² = LM² + KL² - 2×KL×LM×cos(∠M) = 16² + 40² - 2×16×40×cos(135°)

KM² = 2761.0967

KM = √(2761.0967) = 52.55 units.