Question

Triangle ABC has angle measures as shown.

(a) What is the value of x? Show your work.
(b) What are the values of the two unknown angles? Show your work.

Answer 1

As with any triangle, the sum of angles is 180°.

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


(b)
Angle A = x -5 = 30 -5 = 25

Angle B = 3x +30 = 3*30 +30 = 120