Help. Examine the figure below. Determine which of the following angle measures are correct PICK up 2 answers

RPQ = 30 and QRP = 75

Step-by-step explanation:

First we need to find "x".

Since we know that all the angles of a triangle must equal 180 and we know that angles PQR and QRP are the same (Due to the fact that two of the lengths of the triangle are the same) we can set up an equation.

x + (2x + 15) + (2x + 15) = 180

1. we can drop the parentheses (when there is a + in front of an expression in parentheses, the expression remains the same)

x + 2x + 15 + 2x + 15 = 180

2. We can collect the like terms to simplify the equation. (x and 2x and 2x combine to equal 5x) (Remember that there is a hidden 1 behind an "x" without a number next to it)

(the two 15's add together to make 30)

This leaves us with this equation

5x + 30 = 180

3. Now we suptract the constant from 180 (The constant is 30)

5x = 180 - 30

5x = 150

4. Now we devide both sides by 5

x = 30

Next we can find all of the angles

PRQ = (2x + 15)

1. PRQ = (2(30) + 15)

2. PRQ = (60 + 15)

3. PRQ = 75

RQP = (2x + 15)

1. RQP = (2(30) + 15)

2. RQP = (60 + 15)

3. RQP = 75

RPQ = x

RPQ = 30

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

the answer is 21%.