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?
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.