Final answer:
To find the value of x given that <1 and <2 are vertical angles with m<1 = (5x + 1) and m<2 = (4x+3), set the expressions for the angles equal and solve for x. The calculations show that x = 2.
Step-by-step explanation:
The student is tasked with finding the value of x given that <1 and <2 are vertical angles with measures m<1 = (5x + 1) and m<2 = (4x+3). Vertical angles are congruent, meaning they have equal measures. To solve for x, set the expressions for the measures of the angles equal to each other and solve the resulting equation.
m<1 = m<2
5x + 1 = 4x + 3
To find the value of x, subtract 4x from both sides:
5x - 4x + 1 = 4x - 4x + 3
x + 1 = 3
Now, subtract 1 from both sides to isolate x:
x = 3 - 1
x = 2
The value of x is 2.