Question

Use the image shown to determine the values below: (Only type in numbers)

Answer 1

x = 12

m∠UTS = 87

m∠TSR = 143

Explanation:

We know that the angles 56, (3 + 7x), and UST, add up to 180, and that UST and (12x - 1) also add up to 180

Therefore we can say UST = 180 - (12x - 1)

and that:

56 + 3 + 7x + (180 - (12x - 1)) = 180

59 + 7x + 180 - 12x + 1 = 180 (combine like terms and distribute negative)

240 - 5x = 180 (subtract 240 from both sides)

-5x = -60 (divide both sides by -5)

x = 12

Therefore,

m∠UTS = 3 + 7(12) = 87

and

m∠TSR = 12(12) - 1 = 143