Answer:
x = 21
Step-by-step explanation:
The angle T is an exterior angle to the ∆RST, so will be equal to the sum of the remote interior angles:
T = 4x° +2x° = 6x°
T is also a same-side exterior angle with the one marked 54°, so is supplementary to that:
T + 54° = 180°
6x° + 54° = 180°
x + 9 = 30 . . . . . . . . divide by 6
x = 21 . . . . . . . . . . . . subtract 9
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<em>Check</em>
The triangle angles are ...
4x = 84°
2x = 42°
unmarked = 54°
Their sum is 84° +42° +54° = 180° . . . as it should be.
