Final answer:
To find the measure of angle RST, we use the given angle expressions and the fact that a straight line measures 180°. By applying the exterior angle theorem and solving for x, we determine the measure of angle RST which is 111°.
Step-by-step explanation:
The question provides information about the angles in a diagram, where QS is extended through point S to point T, and we are given the measures of angles QRS, RST, and SQR as algebraic expressions in terms of x. To find m∠RST, we will use the fact that QRT is a straight line, and the sum of angles on a straight line is 180°.
Here are the given angle measures:
m∠QRS = (x + 8)°
m∠RST = (4x + 11)°
m∠SQR = (x + 13)°
To find m∠RST, we need the measure of angle QRT, which is the exterior angle to triangle ΔQRS. According to the exterior angle theorem, m∠QRT = m∠QRS + m∠SQR.
Substitute the given expressions:
m∠QRT = (x + 8)° + (x + 13)°
m∠QRT = 2x + 21°
Since QRT is a straight line, m∠QRT + m∠RST = 180°.
2x + 21° + (4x + 11)° = 180°
Combine like terms:
6x + 32° = 180°
Solve for x:
6x = 148°
x = 24.6667, which is approximately 25° (we can round off since angle measures are usually to the nearest degree).
Now, substitute x back into the expression for m∠RST:
m∠RST = (4x + 11)°
m∠RST = (4(25) + 11)°
m∠RST = (100 + 11)°
m∠RST = 111°
Therefore, the measure of angle RST is 111°. The option that corresponds to this result in the provided options would be option C, if we consider 'ZRST' to be a typo for 'RST'.