Final answer:
To find the measure of angle 1, we use the fact that angles 7 and 1 are corresponding angles and thus equal because lines j and k are parallel. After setting their algebraic expressions equal to each other and solving for x, we find that m∠1 is approximately 16.92°.
Step-by-step explanation:
The question deals with parallel lines and angles formed by a transversal. Since lines j and k are parallel, corresponding angles are equal. Thus, the measure of angle 7 (m∠7) and the measure of angle 1 (m∠1) will be equal because they are corresponding angles. We are given:
- m∠7 = (7x + 1)°
- m∠1 = (20x − 10)°
Setting them equal to each other gives us:
7x + 1 = 20x − 10
Now, we solve for x:
13x = 11
x = 11 / 13
Finally, plug x back into the equation for m∠1 to find the measure of angle 1:
m∠1 = 20(11 / 13) − 10
m∠1 = 220 / 13 − 10
m∠1 ≈ 16.92°
Therefore, m∠1 is approximately 16.92°.