Question

HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

Answer 1

Given:

In triangle $EFG, m\angle E = 5x, m\angle F=6x$ and extirior angle G  is 110 degrees.

To find:

The measure of angle FEG.

Solution:

Exterior angle theorem, the sum of two interior angles of a triangle is equal to the opposite extirior angle.

Using extrior angle theorem in triangle EFG, we get

$m\angle E+m\angle F=\text{Measure of extirior angle }G$

$5x+6x=110^\circ$

$11x=110^\circ$

$x=\dfrac{110^\circ}{11}$

$x=10^\circ$

Now,

$m\angle FEG=5x$

$m\angle EFG=5(10^\circ)$

$m\angle EFG=50^\circ$

Therefore, the measure of angle FEG is 50 degrees. So, option C is correct.