Question

In AEFG, EG is extended through point G to point H, m_EFG = (2x + 1)", m_FGH = (6x + 2)°, and mZGEF = (x + 19)°. Find mZGEF.

Answer 1

`m\angle GEF\text{ = 25}`

Here, we want to find the measure of an angle

To do this, we need to get the correct diagrammatic representation

We have this as follows;

To get the measure of any angle, we need the value of x

To get the value of x, we have to use an important triangle theorem

The theorem is that the sum of opposite interior angle equals the exterior angle

We have this as follows;

`\begin{gathered} (2x+1)\text{ + (x+19) = 6x + 2} \\ 2x+1+x+19\text{ = 6x+2} \\ 3x+20\text{ = 6x+2} \\ 6x-3x\text{ = 20-2} \\ 3x\text{ = 18} \\ x\text{ = }(18)/(3) \\ x\text{ = 6} \end{gathered}`

From the question, we are given that the angle GEF is (x+19)

We have to substitute for the value of x here

We have this as;

`x+19\text{ = 6+19 = 25}`