Question

select the correct answer.
rhombus efgh is shown. what is the measure of ∠hgj?
a. 12°
b. 35°
c. 55°
d. 70°

Explanation:

Step1: Use the property of rhombus

In a rhombus, the diagonals bisect the angles. So, \(5x - 5=x + 23\)

Step2: Solve the equation for \(x\)

\(5x-x=23 + 5\)
\(4x=28\)
\(x = 7\)

Step3: Find \(\angle FGH\)

Substitute \(x = 7\) into \((x + 23)^{\circ}\), \(\angle FGH=(7 + 23)^{\circ}=30^{\circ}\)

Step4: Find \(\angle HGJ\)

Since the diagonal \(FJ\) bisects \(\angle FGH\), \(\angle HGJ=\frac{1}{2}\angle FGH\)
\(\angle HGJ=\frac{1}{2}\times70^{\circ}=35^{\circ}\)

Answer:

B. \(35^{\circ}\)