Question

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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=(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.