Question

One fifth of the sum of two angles is 24' and half their difference is 14". Find the two angles.​

Answer 1

Step-by-step explanation:

Two angles; A & B

One fifth of the sum of two angles is 24 degree"

.2(A + B) = 24

Multiply by 5:

A + B = 5(24)

A + B = 120

half of their difference is 14 degree."

.5(A - B) = 14

Multiply by 2

A - B = 2(14)

A - b = 28

Add the two equations

A + B = 120

A - B = 28

--------------Addition eliminates B, find A

2A = 148

A = 148/2

A = 74 degrees

Find B

74 + B = 120

B = 120 - 74

B = 46 degrees

Check solution in the statement:

half of their difference is 14 degree.

.5(74 - 46) =

.5(28) = 14