Question

Need some math help 50pts

Answer 1

angle 1 and 3 are 127.3 degrees and angle 2 is 52.7 degrees

Explanation:

so angle 2 is also 52.7 degrees because angle 2 and 4 are vertical oppostite angles

so we can look at it now that we have to find angle 1. since we know a line is 180 degrees we make angle 1 plus angle 2 equal to 180

let angle 1 be x

x + 52.7 = 180

x = 180 - 52.7

x = 127.3

Answer 2

m∠1 = 127.3°

m∠2 = 52.7°

m∠3 = 127.3°

Explanation:

Vertical Angle Theorem: When two straight lines intersect, the opposite vertical angles are always equal to each other.

⇒ m∠1 = m∠3 and m∠2 = m∠4

If m∠4 = 52.7° then m∠2 = 52.7°

Linear pair: Two adjacent angles which sum to 180°.

⇒ m∠1 + m∠2 = 180°

⇒ m∠3 + m∠4 = 180°

⇒ m∠3 + 52.7° = 180°

⇒ m∠3 = 180° - 52.7°

⇒ m∠3 = 127.3°

As m∠1 = m∠3 then m∠1 = 127.3° also.