Final answer:
To find the measures of angle 1 and angle 5, we solve the equations m∠1 = 4x - 30 and m∠5 = 2x + 50. Assuming the angles are equal, we solve for x and find that both angles measure 130 degrees.
Step-by-step explanation:
To find the measure of angle 1 (m∠1) and angle 5 (m∠5), we need to set up and solve an equation based on the given expressions for each angle. The problem states that m∠1 = 4x - 30 and m∠5 = 2x + 50. It is not specified if angles 1 and 5 are related in any particular way (such as vertical angles or supplementary angles), so we cannot assume any relationship without more information. However, assuming we are given that they are equal (which is a common scenario), we would solve the equation 4x - 30 = 2x + 50.
Let's solve this equation:
- Subtract 2x from both sides: 2x - 30 = 50
- Add 30 to both sides: 2x = 80
- Divide both sides by 2: x = 40
Now, substitute x = 40 back into the original expressions:
- m∠1 = 4(40) - 30 = 160 - 30 = 130
- m∠5 = 2(40) + 50 = 80 + 50 = 130
Therefore, the measures of angle 1 and angle 5 are both 130 degrees.