Question

given rhombus klmn below, m∠mno = 31°. if m∠kno = (-10x + 1)°, solve for x.

Explanation:

Step1: Recall rhombus angle property

In a rhombus, the diagonals bisect the angles. So \( \angle KNO=\angle MNO \).

Step2: Set up equation

Given \( m\angle MNO = 31^\circ \) and \( m\angle KNO=(-10x + 1)^\circ \), we have \( -10x + 1=31 \).

Step3: Solve for \( x \)

Subtract 1 from both sides: \( -10x=31 - 1=30 \).
Divide both sides by -10: \( x=\frac{30}{-10}=- 3 \).

Answer:

\( x = -3 \)