Question

Angles 1 and 2 are complementary and congruent. what is the measure of angle 1? 30° 45° 50° 75°What is the answer?

Answer 1

angle 1 is 45 degrees

Answer 2

see the attached figure to better understand the problem

we know that

1) If angle 1 and angle 2 are complementary angles

then

m∠1+m∠2=
`90\°` ------> equation A

2) If angle 1 and angle 2 are congruent angles

then

m∠1=m∠2 ------> equation B

Substitute equation B in equation A

m∠1+(m∠1)=
`90\°`

2m∠1=
`90\°`

m∠1=
`45\°`

therefore

the answer is

`45\°`