Question

Find the measure of angle QST

Answer 1

qst 115

Explanation:

sum of a triangle add up 180

Answer 2

∠QST = 115°

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:

`(11x)/(11) = (55)/(11)`

x = 5

As ∠QST = 23x, we can substitute in the known x:

23x =

23(5) =

23 * 5 = 115

So ∠QST = 115°

Hope this helps!