Two adjacent angles form a resulting angle with measure 160°. m∠1 = 3x° and m∠2 = (2x+10)°. Solve for x. What are the two unknown angles' measurements? (1 point)
Fill in the blacks.
m∠1 = __°, m∠2 = __°
m∠1 = 3x°, m∠2 = (2x+10)°
According to the given information, the resulting angle is 160°. This means that the sum of the two adjacent angles must be 160°.
m∠1 + m∠2 = 160°
Substituting the given equations:
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 substitute the value of x back into the original equations to find the measurements of the two unknown angles:
m∠1 = 3x = 3(30) = 90°
m∠2 = (2x+10) = 2(30)+10 = 70°
Therefore, the two unknown angles' measurements are:
m∠1 = 90°, m∠2 = 70°.