Two adjacent angles from a resulting angle with measure 160. m∠1 = 3x and m∠2 = (2x + 10) . Solve for x. What are the two unknown angles' measurements?

Answer 1

Since ∠1 and ∠2 are adjacent angles, their measures sum up to the measure of the resulting angle, which is 160. Thus, we have the equation:

∠1 + ∠2 = 160

Substituting in the given expressions for ∠1 and ∠2:

3x + (2x + 10) = 160

Simplifying the equation:

5x + 10 = 160
5x = 160 - 10
5x = 150
x = 150 / 5
x = 30

Now that we have found the value of x, we can substitute it back into the expressions for ∠1 and ∠2 to find their measures:

∠1 = 3x = 3 * 30 = 90
∠2 = 2x + 10 = 2 * 30 + 10 = 60 + 10 = 70

Therefore, the measure of ∠1 is 90 degrees and the measure of ∠2 is 70 degrees.