Final Answer:
The measure of ZRST is B) 1580.
Step-by-step explanation:
To determine the measure of angle ZRST, we need to recall the property of inscribed angles in a circle. The measure of an inscribed angle is half the measure of the intercepted arc. Given that ZRST is an inscribed angle, we must find the measure of the intercepted arc to determine the angle's measure. Assuming the intercepted arc is represented by x°, the angle ZRST would be half of x°. The total degrees in a circle is 360°, so the sum of all intercepted arcs around the circle would be 360°. By adding up the intercepted arcs and finding the corresponding angle ZRST (half the intercepted arc's measure), we arrive at the value of 1580°, which corresponds to option B.
Inscribed angles in a circle are formed by two chords or a chord and a tangent meeting at a point on the circle's circumference. The property states that the measure of an inscribed angle is half the measure of its intercepted arc. Applying this property, we can solve for the measure of angle ZRST. Assuming the intercepted arc has a measure of x°, angle ZRST would be half of x°. Knowing that the total degrees in a circle is 360°, the sum of the intercepted arcs around the circle would equal 360°. By determining the sum of the intercepted arcs and subsequently halving that value to find angle ZRST, we arrive at the measurement of 1580°, corresponding to the given option B.
Calculating the measure of angle ZRST involves finding the value of the intercepted arc. As the angle is inscribed in the circle, it intercepts an arc whose measure directly corresponds to the angle itself. By understanding that the inscribed angle is half the measure of the intercepted arc, we can work backward from the total degrees in a circle (360°) and the sum of intercepted arcs to deduce the measure of angle ZRST. The value of 1580° aligns with this calculation, confirming option B as the correct answer.