Question

What is m angle RST in degrees?

Answer 1

Answer:  $120^{\circ}$

Step-by-step 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°

Step-by-step 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