Question

question 10
6.67 pts
fghi is a rhombus. find m ∠hgi
(7x - 1)°
(4x + 3)°

Explanation:

Step1: Use rhombus diagonal property

Diagonals bisect angles: $\angle IFG = \angle HFG = (7x - 1)^\circ$, $\angle FIG = \angle HIG = (4x + 3)^\circ$.

Step2: Sum adjacent angles to 180°

$2(7x - 1) + 2(4x + 3) = 180$. Simplify: $14x - 2 + 8x + 6 = 180 \Rightarrow 22x + 4 = 180 \Rightarrow 22x = 176 \Rightarrow x = 8$.

Step3: Calculate $\angle HGI$

$\angle HGI = \angle HIG = 4x + 3 = 4(8) + 3 = 35$.

Answer:

35