If three of the interior angles of a convex hexagon each measure 140°, a fourth angle measures 84°, and the measure of the fifth angle is 3 times the measure of the sixth angle, find the measure of the sixth angle.

Sure, let's solve this step by step:

1. We know that the sum of the interior angles of a hexagon is 720°. This is because a hexagon can be divided into 4 triangles, and the sum of the interior angles of a triangle is 180°. So, 4 * 180° = 720°.

2. We know that three of the angles are each 140°, so that's 3 * 140° = 420°.

3. We also know that a fourth angle is 84°.

4. So, the sum of the first four angles is 420° + 84° = 504°.

5. That means the sum of the last two angles must be 720° - 504° = 216°.

6. We're told that the fifth angle is 3 times the sixth angle. Let's call the sixth angle x. That means the fifth angle is 3x.

7. So, x + 3x = 216°.

8. That simplifies to 4x = 216°.

9. So, x = 216° / 4 = 54°.

So, the measure of the sixth angle is 54°.

Sure, let's solve this step by step:

Step 1: We know that the sum of the interior angles of a hexagon is 720°.

Step 2: We know that three of the angles are each 140°, so that's 3*140 = 420°.

Step 3: We also know that a fourth angle is 84°. So, the total of four angles is 420 + 84 = 504°.

Step 4: This leaves us with 720 - 504 = 216° for the last two angles.

Step 5: We know that the fifth angle is 3 times the sixth angle. Let's call the sixth angle x. So, the fifth angle is 3x.

Step 6: Therefore, we can set up the equation x + 3x = 216.

Step 7: Solving this equation gives us 4x = 216, so x = 216 / 4 = 54°.

So, the measure of the sixth angle is 54°.