If the interior angles of a triangle are 15, 15(x+y), and 25y and the relation between x and y is given by 5x-4y+2=0, then what is the measure of the smallest angle of the triangle

The sum of 3 angles inside a triangle is 180 deg, then:

=> 15 + 15(x + y) + 25y = 180

=> 15x + 40y = 165   (1)

And we have:

5x - 4y + 2 = 0

=> 5x - 4y = -2

=> 15x - 12y = -6       (2)

From (1) and (2), we have:

52y = 171

=> y = 171/52

=> 5x - 4 x 171/52 = -2

=> 5x = -2 + 171/13

=>  x = 145/65

=> First angle: 15 deg

=> Second angle: 15*(145/65 + 171/13) = 82.788 deg

=> Third angle = 25 x 171/52 = 82.211

=> Minimum angle: 15 deg

Hope this helps!

:)

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.

you'll just earn points here

step-by-step explanation: