Answer:
∠QST = 115°
Step-by-step explanation:
Because all angles on a straight line must add to 180 and so should the total angles in a triangle:
∠UST + 23x = 180
And:
∠UST + 12x + 55 = 180
So knowing this, ∠U + ∠T must add up to 23x because 180 - ∠UST is the same for both above equations:
55 + 12x = 23x
Subtract 12x from both sides to isolate the 55 and 23x:
55 + 12x - 12x = 23x - 12x
55 = 11x
Divide both sides by 11:
[tex]\frac{11x}{11} = \frac{55}{11}[/tex]
x = 5
As ∠QST = 23x, we can substitute in the known x:
23x =
23(5) =
23 * 5 = 115
So ∠QST = 115°
Hope this helps!
