Question

What is m angle RST in degrees?

Answer 1

Answer:
`120^(\circ)`

Explanation:

Given: The measure of ∠RST is represented by the expression:
`(6x+12)^(\circ)`

Also, ∠RSU=
`78^(\circ)`

∠UST=
`(3x-12)^(\circ)`

From the figure it can be seen that:-

`\angle{RST}=\angle{RSU}+\angle{UST}\\\\\Rightarrow\ (6x+12)^(\circ)=78^(\circ)+(3x-12)^(\circ)\\\\\Rightarrow\ 6x-3x=78-12-12\\\\\Rightarrow\ 3x=54\\\\\Rightarrow\ x=18`

Now, the measure of ∠RST will be :
`(6(18)+12)^(\circ)=120^(\circ)`

Answer 2

Answer: m∠RST = 120°

Explanation:

m∠RST = m∠RSU + m∠UST

6x+12 = 78 + 3x-12

3x = 78-24 = 54

x = 54/3 = 18

m∠RST = (6x+12)° = (108+12)° = 120°

Check: 120 must equal 78+3×18-12

78+54-12 = 132-12 = 120