Answer:
127.5
Step-by-step explanation:
First, we need to find the value of x
since the two angles are connected to a straight line, their sum will be 180 (degrees)
[tex](2x+7)+(6x-9)=180^{o}[/tex]
add the angles together
[tex]\therefore 8x-2=180[/tex]
add 2 to both sides
[tex]\therefore 8x=182[/tex]
divide out by 8
[tex]\therefore x = 22.75[/tex]
now we must determine which angle has the greater value (not visually)
[tex]angle A = 2x+7[/tex]
[tex]\therefore \angle{A} = 2(22.75)+7[/tex]
[tex]\therefore \angle{A} = 45.5+7[/tex]
[tex]\therefore \angle{A} = 52.5[/tex]
[tex]angle B = 6x-9[/tex]
[tex]\therefore \angle{B} = 6(22.75)-9[/tex]
[tex]\therefore \angle{B} = 136.5-9[/tex]
[tex]\therefore \angle{B} = 127.5[/tex]
[tex]\angle{B}>\angle{A}\ \because\ 127.5>52.5[/tex]
so the answer would be 127.5
