Question

1. find the measure of each unknown angle

Explanation:

Step1: Calculate total interior angles

For a 7-sided polygon, total interior angles = $(7-2)\times180^\circ = 900^\circ$

Step2: Sum all given angles

$$(-2x) + 127 + (84 - x) + 120 + 135 + (-x + 47) + 147 = 900$$

Step3: Simplify the left side

Combine like terms:
$$-2x -x -x + 127 + 84 + 120 + 135 + 47 + 147 = 900$$
$$-4x + 660 = 900$$

Step4: Solve for $x$

$$-4x = 900 - 660$$
$$-4x = 240$$
$$x = \frac{240}{-4} = -60$$

Step5: Calculate each unknown angle

• $\angle A = -2x = -2(-60) = 120^\circ$
• $\angle C = 84 - x = 84 - (-60) = 144^\circ$
• $\angle F = -x + 47 = -(-60) + 47 = 107^\circ$

Answer:

$\angle A = 120^\circ$, $\angle C = 144^\circ$, $\angle F = 107^\circ$