Question

Question 4Given AGEO 2 AFUMZE = (42.)in/N = 40mZU = 80ånd m_G = 60find the value of a(The problem is sort of messed up because of canvas)

Answer 1

It is stated in the problem that ΔGEO is congruent with ΔFUN. On the first triangle, the measurement of angle E and angle G is given but the measurement of angle O is not given. Using the congruence relation of the two triangles, it is true that

`m\angle O\cong m\angle N`

The measurement of angle N is provided in the problem, which is equal to 40 degrees. Hence, we can say that angle O has also an angle measurement of 40 degrees base on the statement above.

The sum of the interior angles of the triangle is equal to 180 degrees. This means that if we add up the interior angles of the triangle GEO, we have the following equation

`m\angle G+m\angle E+m\angle O=180`

Substitute the measurement of each angle on the equation above and compute, we get

`\begin{gathered} 60+4x+40=180 \\ 4x+100=180 \\ 4x=180-100 \\ (4x)/(4)=(80)/(4) \\ x=20 \end{gathered}`

Therefore, the value of x is equal to 20 degrees.