Final answer:
After calculating the sum of angles in triangle RST and solving for x, the measure of angle R is found to be 46 degrees (rounded to the nearest whole number). There seems to be a disparity with the given answer choices as none match this result.
Step-by-step explanation:
To find the measure of angle R in triangle RST, we use the fact that the sum of the angles in a triangle is always 180 degrees. We have the given angle expressions:
- m∠R = (6x-4)°
- m∠S = (10x-9)°
- m∠T = (8x-7)°
Let's set up an equation with these expressions:
(6x-4)° + (10x-9)° + (8x-7)° = 180°
In combining like terms, we get:
24x - 20 = 180
Now we can solve for x:
24x = 200
x = 200 / 24
x = 8.333...
Finally, we'll substitute x back into the expression for angle R:
m∠R = 6x - 4
m∠R = 6(8.333...) - 4
m∠R = 50 - 4
m∠R = 46° (rounded to nearest whole number)
However, none of the answer choices match 46° exactly. There may be a mistake in the given answer choices or a rounding error, but based on the calculations performed, the closest correct answer, when rounding to the nearest degree, should be 46°.