Question

If m<1 is the supplement of m<2 and the measure of each angle is given:

m<1=2x+65
m<2=3x-25

Find m<1:

Answer 1

m<1 = 121°

m<2 = 59°

Explanation:

If m<1 is the supplement of m<2 and the measure of each angle is given:

m<1=2x+65

m<2=3x-25

Find m<1:

When two angles are supplement of each other, there sum is equal to 180°

i.e m<1 + m<2 = 180°

Putting values and finding angle 1

`2x+65+3x-25=180\\5x+40=180\\5x=180-40\\5x=140\\x=(140)/(5)\\x=28`

So, we get x=28

Now finding m<1 by putting x=28

`m<1=2x+65\\m<1=2(28)+65\\m<1=56+65\\m<1=121^(\circ)\\`

Now, finding m<2 by putting x=28

`m<2=3x-25\\m<2=3(28)-25\\m<2=84-25\\m<2=59^(\circ)`

So, we get:

m<1 = 121°

m<2 = 59°