Answer:
A) m∠QTS = 20°
B) The degree measure of minor arc QS is 40°
C) The degree measure of arc QTS is 320°
Step-by-step explanation:
* Lets revise some facts about the circle
- The inscribed angle in a circle is the angle whose vertex lies on the
circumference of the circle and its sides are the chords in the circle
- Each inscribed angle subtended by an opposite arc to its vertex
- The measure of the arc is twice the measure of the inscribed angle
subtended by this arc
- The measures of the inscribed angles subtended by the same arcs
are equal
- The measure of the circle is 360°
* Lets solve the problem
- In circle U
A)
∵ ∠QPS is an inscribed angle subtended by arc QS
∵ ∠QTS is an inscribed angle subtended by arc QS
∴ m∠QPS = m∠QTS
∵ m∠QPS = 20°
∴ m∠QTS = 20°
B)
- Lets find the measure of the arc QS
∵ ∠QPS is an inscribed angle subtended by arc QS
∵ The measure of the arc is twice the measure of the inscribed angle
subtended by this arc
∴ Measure of arc QS = 2 × m∠QPS
∵ m∠QPS = 20°
∴ Measure of arc QS = 2 × 20° = 40°
∴ The degree measure of minor arc QS is 40°
C)
∵ The arc QTS is an major arc
∵ The sum of the major arc QTS and the minor arc QS equals the
measure of the circle
∵ The measure of the circle is 360°
∴ m of major arc QTS + m of minor arc QS = 360°
∵ m of minor arc QS = 40°
∴ m of major arc QTS + 40° = 360°
- Subtract 40° from both sides
∴ m of major arc QTS = 320°
∴ The degree measure of arc QTS is 320°
