Question

HELP PLEASEEEEEEEEEEEEEEEEEEE!!!!!!!!! HURRY IM BEING TIMED!!!

Answer 1

GiveN:-

• 
  `\sf \: m \angle \: 2 = 111 \degree`

To finD:-

• 
  `\sf \: m \angle \: 1= ??`
• 
  `\sf \: m \angle \: 3= ??`
• 
  `\sf \: m \angle \: 4= ??`

SolutioN :-

As we know that angle
`\sf \: m \angle \: 2` is equal to angle
`\sf \: m \angle \: 4` (because they are vertically off opposite angle).

So,

`{ \longrightarrow { \pmb{\: \: m \angle \: 4 \: =m \angle \: 2 }}}`

`{ \longrightarrow { \pmb{\: \: m \angle \: 4 \: =111 \degree }}}`

Now,

we know that sum of
`\sf \: m \angle \: 4` and
`\sf \: m \angle \: 1` is equal to 180° , as they are lying on one plane

`{ \longrightarrow { \pmb{\: \: m \angle \: 4 \: + m \angle \: 1 = 180 \degree }}}`

`{ \longrightarrow { \pmb{\: \: 111 \degree \: + m \angle \: 1 = 180 \degree }}}`

`{ \longrightarrow { \pmb{\: m\angle \: 1 = 180 \degree - 111 \degree \:}}}`

`{ \longrightarrow { \pmb{\: m\angle \: 1 = 69 \degree \:}}}`

Again, angle
`\sf \: m \angle \: 1` is equal to angle
`\sf \: m \angle \: 3` (because they are vertically off opposite angle).

`{ \longrightarrow { \pmb{\: m\angle \: 1 = m\angle \: 3 \:}}}`

`{ \longrightarrow { \pmb{\: m\angle \: 3 = 69 \degree \:}}}`

Therefore:-

• 
  `\sf \: m \angle \: 1= 69°`
• 
  `\sf \: m \angle \: 3= 69°`
• 
  `\sf \: m \angle \: 4= 111°`