Question

PLZ HURRY Part A:

Find the measure of the following angles:

<1

<2

<3.


Show your work to justify your answers. Earn up to 1 point for each missing angle with the correct answer and work shown.


Part B:

Answer the following question in 1-2 complete sentences. How is the measure of <1 and the measure of <2 related to the exterior 123° angle?

Answer 1

Explanation:

(A) From the given figure, we have

`{\angle}1+92^(\circ)=180^(\circ)` (Linear pair)

⇒
`{\angle}1=180^(\circ)-92^(\circ)`

⇒
`{\angle}1=88^(\circ)`

Thus, the measure of
`{\angle}1` is
`88^(\circ)`.

Also, using the angle sum property in the given triangle, we get

`{\angle}1+{\angle}2+57^(\circ)=180^(\circ)`

⇒
`88^(\circ)+{\angle}2+57^(\circ)=180^(\circ)`

⇒
`{\angle}2+145^(\circ)=180^(\circ)`

⇒
`{\angle}2=35^(\circ)`

Thus, the measure of
`{\angle}2` is
`35^(\circ)`.

And,
`{\angle}2+{\angle}3=180^(\circ)`

⇒
`35^(\circ)+{\angle}3=180^(\circ)`

⇒
`{\angle}3=145^(\circ)`

Thus, the measure of
`{\angle}3` is
`145^(\circ)`.

(B) Exterior angle theorem states that the exterior angle is equal to the sum of the two interior angles, thus from the given figure, we have

`{\angle}1+{\angle}2=123^(\circ)`

Therefore, the relationship between the measure of
`{\angle}1` and
`{\angle}2` to exterior angle is
`{\angle}1+{\angle}2=123^(\circ)`.

Answer 2

<1:88

<2:65

<3:115

Explanation:

Since we know that a line and the inside of a triangle equals 180 than we can use that to identify the missing angles.Using what we know about a line we can subtract 92 from 180 and we get 88, knowing that angle 1(<1)is the only angle that rest on that line than we know that <1 is 88.(to check this you can add 92 plus 88 and you get 180)Then switching hands,we can now figure out the interior missing angle 2(<2).There are two ways you can do this,Add all the interior angles together and then subtract from 180(88+57=145 then 180-145=35)or you can subtract all the known interior angles and then the answer is your missing angle(180-57-88=35).Now switching again, in order to find <3 then you have to find which number falls on the angle which we are looking for.Which would be 35 or <2.Now all you have to do is subtract 180-35=145

Part B:

I agree with the other person below⬇⬇⬇