A quadrilateral has two angles that measure 238° and 100°. The other two angles are in a ratio of 5:6. What are the measures of those two angles?

10 degrees and 12 degrees

Step-by-step explanation:

The first step is to establish the measure of the sum of the other two degrees and since the sum of all angles in a quadrilateral is 360 degrees we find:

360-238-100=22 and since the ratio of the two angles is 5:6 we can split 22 into 5 and 6 pieces of equal measure (their measure will be represented as x) to find: 5x+6x=22; 11x=22; x=2

And to find the measures: Measure of angle one (the smaller angle) is 5*2=10

Measure of angle two (the larger angle): 6*2=12

And to check the answer check that:

10/12=5/6 (checking the ratio); 10+12+238+100=360 (checking if it is a quadrilateral)

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0