Question

Angles ABC and CBD are complementary. Angle CBD is 9 degrees more than half of angle ABC. What are the measurements of the two angles?

Answer 1

`54^@"and "36^@`

Explanation:

`"let "angleABC=x`

`"then "angleCBD=1/2x+9`

`"the angles are complementary hence sum to "90^@`

`rArrx+1/2x+9=90`

`rArr3/2x=90-9=81`

`rArr3/2x=81`

`"multiply both sides by "2/3`

`cancel(2)/cancel(3)xxcancel(3)/cancel(2)x=2/cancel(3)^1xxcancel(81)^(27)=2xx27=54`

`rArrx=angleABC=54^@`

`rArrangleCBD=1/2x+9=1/2xx54+9=36^@`