Question

Three of the exterior angles of a hexagon have a sum of 240 degrees. The remaining exterior angles are congruent to each other. Determine the measure of the remaining angles

Answer 1

Answer:40 degrees

Step-by-step explanation:360(total angle)-240(given)=120

6(sides)-3(given)=3

120/3=40

Answer 2

Given: Sum of three exterior angles of a hexagon = 240°

           (Remaining three angles are congruent to each other.)

To find: Measure of remaining angles

Let: Each of the remaining angle be $x$ (these are congruent to each other)

Solution:

∵ Sum of exterior angles of a hexagon = 360°

Now, given that three of these angles have sum of 240°

Sum of rest three angles = 360° - 240° = 120°

Also, given that rest three angles are congruent to each other which means these have same measure.

⇒ $x + x + x = 120$

⇒ $3x = 120$

⇒ $x = \frac{120}{3} = 40$

Hence, measure of each of the remaining angles is 40°.