Question

What are the missing angle measures in triangle ABC?

1.4° and 88.6°
18.6° and 71.4°
35.5° and 54.5°
44.4° and 45.6°

Answer 1

35.5° and 54.5°

solve though tangent

Answer 2

we know that

In the right triangle ABC

∠
`A+`∠
`B=90` ------> by complementary angles

so

Step
`1`

Find the measure of angle B

we know that

`tan\ B=(opposite\ side\ angle\ B)/(adjacent\ side\ angle\ B)`

in this problem

`opposite\ side\ angle\ B=7in\\ adjacent\ side\ angle\ B=5in`

so

`tan\ B=(7)/(5) \\ \\ B=arc\ tan(7)/(5) \\ \\ B=54.5\ degrees`

Step
`2`

Find the measure of angle A

`A+B=90\\ A=90-B\\ A=90-54.5\\ A=35.5\ degrees`

therefore

the answer is the option

35.5° and 54.5°