Answer: m = 39
Explanation:
To find the value of m in the given pentagon, let's use the properties of exterior angles of polygons and the sum of interior angles of a pentagon.
1. The sum of the exterior angles of any polygon is always 360°.
2. The sum of the interior angles of a pentagon is always 540°.
Let's start by finding the measure of the three known angles:
- One exterior angle is given as 60°.
- Two other exterior angles are (90 - m)° each.
To find the remaining two exterior angles, we can subtract the sum of the known angles from 360°:
(90 - m)° + (90 - m)° + 60° = 360°
Simplifying the equation:
180° - 2m + 60° = 360°
Combining like terms:
240° - 2m = 360°
Next, let's find the interior angles of the pentagon:
The remaining interior angles are (30 + 2m)° each.
To find the sum of all interior angles, we multiply the number of sides (pentagon has 5 sides) by the measure of each interior angle:
5 * (30 + 2m)° = 540°
Simplifying the equation:
150° + 10m = 540°
Subtracting 150° from both sides:
10m = 390°
Finally, we can solve for m by dividing both sides of the equation by 10:
m = 390° / 10
m = 39°
Therefore, the value of m is 39°.