Final answer:
To find the measure of angle <1, we use the fact that <1 and <2 are supplementary and set up an equation with their expressions. After solving for x, we get that x = 17, which gives us a measure of 74 degrees for <1.
Step-by-step explanation:
The student's question involves supplementary angles, which are two angles whose measures add up to 180 degrees. Given that m<1 = (5x - 11) and m<2 = (5x+21), and knowing that they are supplementary, we can set up an equation to find the value of x:
m<1 + m<2 = 180°
(5x - 11) + (5x + 21) = 180°
10x + 10 = 180°
10x = 170°
x = 17°
Once we have the value of x, we substitute it back into the equation for m<1 to find its measure:
m<1 = 5x - 11
m<1 = 5(17) - 11
m<1 = 85 - 11
m<1 = 74°
Therefore, the measure of <1 is 74 degrees.