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: 2x^2 +3x+15 and 3x^2+x-20

Find all possible measures of angle BED.

Answer provided by our tutors

2x^2 + 3x + 15 = 3x^2 +x -20

x^2-2x-35 = 0

x=7 or x =-5

when x =7 angle AED and CEB are

3(7)^2 +7 -20 = 134

2(7)^2  +3* 7  +15 =134

sum of other 2 angles =92

angle BED =92/2 =46

when x= -5 angle AED and CEB are

50 degrees each

sum of other 2 angles =260

angle BED =260/2 =130

so the possible measures of angle BED = 46 and 130