Question

3. Triangle ABC has angle measures as shown.

a) What is the value of x? Show your work.

Answer 1

As always, the sum of the measures of the angles in a triangle is 180°.

(x -5) +(3x +30) +35 = 180
4x +60 = 180 . . . . . . . . . . . . . collect terms
4x = 120 . . . . . . . . . . . . . . . . . subtract 60
x = 30 . . . . . . . . . . . . . . . . . divide by 4

a) The value of x is 30.

Answer 2

The sum of the angles in a triangle is 180°, therefore:
$(x - 5) + (3x + 30) + 35 = 180$
$x - 5 + 3x + 30 + 35 = 180$
Sum up x + 3x
$4x - 5 + 30 + 35 = 180$
Sum up all the numbers
$4x + 60 = 180$
Substract 60 from both sides
$4x = 120$
And finally divide by 4 (on both sides)
$x = 30$