Question

find the value of x
1. two vertical angles have measure: x squared+18x and x squared+54.
2. the measures of the angles of a quadrilateral are: x, x+4, x+8 and x+12
3.the lengths of the legs of an isosceles triangle are 7x-13 and 2x+17
4.consecutive angles of a parallelogram have the measures 6x and 2x+20.
5. a trapezoid has bases of length x and x+8 and a median length 15.
Thank you very much!

Answer 1

If two vertical angles have measure x^2+18x and x^2+54, then 2x^2+18x+54=180, so x^2+9x+27=90, and x^2+9x-63=0.  Using the quadratic formula, we see that x is equal to about 4.6.

2.  These measures add to 360, so we have x+x+4+x+8+x+12=360, so 4x+24=360.  Subtracting 24 and dividing by 4, we see that x=84.

3.  The lengths of the legs of an isosceles triangle are equal, so 7x-13=2x+17.  Subtracting 2x and adding 13, we see that 5x=30, so x=6.

4.  Consecutive angles of a parallelogram sum to 180, so 8x+20=180.  Solving, we see that x=20.

5.  The sum of the bases is twice the median, so 2x+8=30, and x=11.