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?

Answer 1

Answer:

s measures 33° and t measures 57°.

Step-by-step 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°.

Answer 2

Answer:

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°.