Question

Help me with #5 pleaseeeeeeeeeee

Answer 1

`\angle 1 = 45` degrees

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:

`60+7x+12+\angle 1=180\\72+7x+\angle 1=180\\7x+\angle 1=108`

Also, straight angle is 180 degrees, thus Angle 1 and (14x + 9) angle is sum to 180, thus we can write:

`14x+9+\angle 1=180\\14x + \angle 1=171`

Or we can write this as:

`14x + \angle 1=171\\\angle 1 = 171 - 14x`

We substitute this expression for Angle 1 into 1st equation we got and solve for x first,

`7x+\angle 1 = 108\\7x+( 171 - 14x)=108\\-7x=-63\\x=9`

Since x = 9, the angle "14x + 9" would be:

14(9) + 9 = 135

Hence Angle 1 would be:

`\angle 1 + 14x + 9 = 180\\\angle 1 + 135 = 180\\\angle 1 = 45`