Angle rqt is a straight angle. what are the measurements of angle rqs and tqs?

The measure of m<RQS and <TQS is 43 and 137degrees respectively.

Geometry is a branch in mathematics that is concerned with the measurement of angles, lines, and properties of triangles.

For the diagram shown, the sum of angle on the straight line TQR is 180degrees. This means that:

m<RQS + m<TQS = 180

Substitute the given angles

2x + 4 + 6x + 20 = 180

8x + 24 = 180

8x = 180 - 24

8x = 156

x = 156/8

x = 19.5

Get the angle m<RQS

Since m<RQS = 2x + 4

m<RQS = 2(19.5)+4

m<RQS = 39 + 4

m<RQS = 43degrees

Recall that:

m<TQS = 180 - m<RQS

m<TQS = 180 - 43

m<TQS = 137degrees

Hence the measure of m<RQS and <TQS is 43 and 137degrees respectively.

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region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true