Answer: 92 degrees
Step-by-step explanation:
Adjacent angles:
(m\angle 2 = 6x + 2^\circ)
(m\angle 3 = 8x - 32^\circ)
We know that adjacent angles are supplementary, which means their sum is 180°:
[ m\angle 2 + m\angle 3 = 180^\circ ]
Substitute the expressions for (m\angle 2) and (m\angle 3):
[ (6x + 2) + (8x - 32) = 180 ]
Combine like terms:
[ 14x - 30 = 180 ]
Add 30 to both sides:
[ 14x = 210 ]
Divide both sides by 14:
[ x = 15 ]
Now, let’s find (m\angle 1):
[ m\angle 1 = 6x + 2 = 6(15) + 2 = 92
