Problema Solution
Ray AB and ray CD intersect at point E. Their intersection forms angle AED and angle CEB, which have measures that can be expressed by these two quadratic equations: 2x2 + 3x + 15 and 3x2 + x - 20
Find all possible measures of angle BED.
Answer provided by our tutors
Angle AED=Angle CEB.
2x^2+3x+15=3x^2+x-20.
3x^2-2x^2+x-3x-20-15=0.
x^2-2x-35=0.
x^2-7x+5x-35=0.
x(x-7)+5(x-7)=0.
(x-7)(x+5)=0.
x=7,-5.
Angle AED =2x2 + 3x + 15.
=2*7^2+3*7+15, 2*(-5)^2+3*-5+15.
134,50.
The possible measures of angle BED are (180-134), (180-50).
=46, 130.