Question

what is the value of v?
f
v
e
43°
g
d
40°
v = °
submit

Explanation:

Step1: Use the property of congruent triangles

Since \(FG = FE\) and \(GD = ED\), and \(GE = GE\) (common side), \(\triangle FGE\cong\triangle DGE\) (by SSS - Side - Side - Side congruence criterion). So \(\angle FEG=\angle DEG = 43^{\circ}\).

Step2: Calculate the sum of angles in \(\triangle DGE\)

In \(\triangle DGE\), \(\angle D = 40^{\circ}\), \(\angle DEG = 43^{\circ}\), then \(\angle DGE=180^{\circ}-\angle D-\angle DEG=180^{\circ}-40^{\circ}-43^{\circ}=97^{\circ}\).

Step3: Use the congruence of angles

Because \(\triangle FGE\cong\triangle DGE\), \(\angle F=\angle DGE\).

Answer:

\(97\)