In the rhombus shown here, the measures of J and K are in the ratio 3:7. What is the measure of JKM?
A. 27°
B. 54°
C. 63° ✓
- we know that , Adjacent angles of a rhombus measure 180°
- Let ∠J be 3x & ∠K be 7x as the ratio between them is 3:7
- ∴ , 3x + 7x = 180°
- 10x = 180°
- x = 180°/10
- x = 18°
- ∵, ∠J = 3x = 3*18° = 54°
- and, ∠K = 7x = 7*18° = 126°
- since,∠JKM = ∠LKM and ∠JKM + ∠LKM = ∠K (the diagonal of a rhombus bisects the angle through which it passes)
- so, ∠JKM = ∠K/2
- ∵∠JKM = 126°/2
- ∠JKM = 63°
D. 126°