Two adjacent angles form a resulting angle with measure 160 degree. m<1 = 3x degree and m<2 = (2x + 10) degree. Solve for x. What are the two unknowns angles measurements?
m<1 = ____degree, m<2 = _____
Since the two angles are adjacent, their measures add up to the measure of the resulting angle. Therefore, we have the equation:
m<1 + m<2 = 160 degrees
Substituting the given expressions for m<1 and m<2, we get:
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 measure of each angle by substituting x = 30 into the given expressions for m<1 and m<2:
m<1 = 3(30) = 90 degrees
m<2 = 2(30) + 10 = 60 + 10 = 70 degrees
Therefore, m<1 = 90 degrees and m<2 = 70 degrees.