Answer:
FIrst, lets set up some rules to keep in mind:
The interior angles of any triangle will add up to 180°
Therefore, m<FED + m<FDE + m<DEF or in other words 64 + 2x+ m<DFE=180
Next, lets note that there are supplementary angles in this problem which are a set of angles that add to 180°. For example, m<HFC + m<EFH + m<DFE = 180.
With those in mind lets solve:
If we find the m<DFE then we can find the value of x since the interior angles of any triangle add to 180.
to find f we can use supplementary angles.
42°+90°+m<DFE=180
132+m<DFE=180
m<DFE=48°
Therefore,
64+48+2x=180
112+2x=180
2x=68
x=34
To check our answer we can plug in 34 for x and the 3 interior angles of that triangle should add to 180
2(34)+64+48=180?
68+64+48=180?
180=180
x=34 is valid
Step-by-step explanation:
