Question

Two angles are complementary. The measure of the larger angle is 30 less than three times the smaller angle . What are the measures of both angles?

Answer 1

Measure of both the angles, `60^0, 30^0`

Explanation:

If two angles are complementary, sum of these two angles is `90^0`
Let larger angle be a and the smaller angle
Given :
`a + b = 90` Eqn (1)

`a = 3b - 30`
`a - 3b = -30` Eqn (2)

Subtracting Eqns (2) from (1),
`a + b - a - (-b) = 90 - 60`
`4b = 120, b = 30^9`

Substituting value of ‘b’ in Eqn (1),
`a + 30 = 90, a = 60^0`

Answer 2

`30^@" and "60^@`

Explanation:

`"let the smaller angle "=x`

`"then the larger angle "=3x-30`

`• " complementary angles sum to "90^@`

`rArrx+3x-30=90`

`rArr4x-30=90`

`"add 30 to both sides"`

`4xcancel(-30)cancel(+30)=90+30`

`rArr4x=120`

`"divide both sides by 4"`

`(cancel(4) x)/cancel(4)=120/4`

`rArrx=30`

`"smaller angle "=x=30^@`

`"larger angle "=3x-30=(3xx30)-30=60^@`