Question

Two complementary angles have measures of `s` and `t`. If `t` is 9 less than twice `s`, what are the measures of each angle?

The value of s and t.
with work explaining.

Answer 1

Two complementary angles have measures of `s` and `t`.

Hence, s+t=90°

`t` is 9 less than twice `s`, t=2s-9

According to the above problem,

→s+t=90

→s+2s-9=90

→3s=99

→s=99/3

→s=33

Therefore, the value of s=33°

and t=2(33)-9 = 66-9 = 57°.

Answer 2

s measures 33° and t measures 57°.

Explanation:

Since the two angles s and t are complementary, this implies that:

`m\angle s+m\angle t=90`

We are given that t is 9 less than twice s. Hence:

`m\angle t=2m\angle s-9`

We can substitute this into the first equation:

`m\angle s+(2m\angle s-9)=90`

Solve for s. Combine like terms:

`3m\angle s-9=90`

Adding 9 to both sides yields:

`3m\angle s=99`

And dividing both sides by 3 gives us that:

`m\angle s=33^\circ`

Returning to our second equation, we have:

`m\angle t=2m\angle s-9`

So:

`m\angle t=2(33)-9=66-9=57^\circ`

So, s measures 33° and t measures 57°.