Two adjacent angels form a resulting angle with measure 160 .m<1=3x and m<2=(2x+10) solve for x what are the two unknown angels measurements?

Answer 1

We have two adjacent angles (angle 1 and angle 2), and their resulting angle measures 160 degrees.

Let's solve for x using the given information:

m<1 = 3x
m<2 = 2x + 10

Since angle 1 and angle 2 are adjacent, their sum should be equal to the resulting angle measure:

m<1 + m<2 = 160

Substituting the equations for m<1 and m<2:

3x + (2x + 10) = 160

Combining like terms:

5x + 10 = 160

Subtracting 10 from both sides:

5x = 150

Dividing both sides by 5:

x = 30

Now, we can find the measurements of angle 1 and angle 2:

m<1 = 3x = 3(30) = 90 degrees

m<2 = 2x + 10 = 2(30) + 10 = 60 + 10 = 70 degrees

Therefore, angle 1 measures 90 degrees and angle 2 measures 70 degrees.