Quadrilateral RSTU, diagonals SU and RT intersect at point V. RSTU is a parallelogram. If m∠TSV = 31° and m∠SVT = 126°, explain how you can find the measure of ∠URV. Show all steps of your work, and refer to any properties of triangles, parallelograms, or triangle congruency theorems as necessary to justify your response.

m∠URV=  23°

Step-by-step explanation:

If we look at the diagram we find that there is a triangle  SVT formed by the diagonals and the base of the parallelogram.

As all the angles of the triangle SVT must be equal to 180 degrees therefore we can find the third angle by adding the other two known angles and subtracting them from 180 degrees.

Hence

m ∠VTS + m∠TSV+ m∠SVT= 180°

m ∠VTS = 180°-31°- 126°

m ∠VTS = 23°

If we extend the diagonal RT and also increase the other lines we find that it acts as a transversal of the lines RU and ST.

As the alternate interior angles of the transversal are equal  the angles

m∠URV=  m ∠VTS  are also equal .

Therefore m∠URV=  23°

as

m ∠VTS=  23°

m∠URV=  m ∠VTS  are alternate angles.

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

10cm

step-by-step explanation:

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