A. what is the degree measure of b. what is the degree measure of minor arc qs
c. what is the degree arc qts?

Measure of <QTS = 20°

Measure or minor arc QS = 40°

Step-by-step explanation:

From the figure we can see a circle with center U.

To find the measure of <QTS

m<QTS = m<QPS   [Angles subtended by same arc are equal]

Therefore m<QTS = 20°

To find the measure of minor arc QS

Measure or minor arc QS = 2 * m<QPS

 = 2 * 20 = 40°

Measure or minor arc QS = 40°

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°

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions