Answer:
[tex]\angle 1 = 45[/tex] degrees
Step-by-step explanation:
Sum of 3 angles in a triangle is 180..
The angles given are:
60
7x + 12
1
So we sum to 180 and write:
[tex]60+7x+12+\angle 1=180\\72+7x+\angle 1=180\\7x+\angle 1=108[/tex]
Also, straight angle is 180 degrees, thus Angle 1 and (14x + 9) angle is sum to 180, thus we can write:
[tex]14x+9+\angle 1=180\\14x + \angle 1=171[/tex]
Or we can write this as:
[tex]14x + \angle 1=171\\\angle 1 = 171 - 14x[/tex]
We substitute this expression for Angle 1 into 1st equation we got and solve for x first,
[tex]7x+\angle 1 = 108\\7x+( 171 - 14x)=108\\-7x=-63\\x=9[/tex]
Since x = 9, the angle "14x + 9" would be:
14(9) + 9 = 135
Hence Angle 1 would be:
[tex]\angle 1 + 14x + 9 = 180\\\angle 1 + 135 = 180\\\angle 1 = 45[/tex]
