A wooden plate is shaped as a pentagon. The measure of one angle is 20°. The remaining interior angles are obtuse and of equal measure.
What is the measure of each obtuse angle in the pentagon?
You know that a pentagon has 5 sides and 5 angles. So, if you already have one angle you only have to solve for four more, which happen to be equal. So, first determine the total degrees sum of the interior angles in a pentagon by using the formula: 180(n-2) where n is the number of sides in the polygon. So, the sum of interior angles in a pentagon is 540. And now that you have one of them, you know the sum of the remaining 4 is 540-20=520 degrees. And the problem also tells you that these last four angles are equal and obtuse! You are halfway done: just divided the remaining degrees, 520/4 and you get 130 degrees. Now check, is this obtuse? Yes, it is greater than 90 degrees but less than 180! Hope this helps!
140
To find the measure of each obtuse angle in the pentagon, we need to use the fact that the sum of the interior angles of any pentagon is 540°.
We know that one angle in the pentagon is 20°. Let's call the measure of each obtuse angle x.
The sum of the measures of all the interior angles in the pentagon can be expressed as follows:
20° + x + x + x + x = 540°
Simplifying this equation, we have:
20° + 4x = 540°
Subtracting 20° from both sides, we get:
4x = 520°
Finally, dividing both sides by 4, we find:
x = 130°
So, each obtuse angle in the pentagon measures 130°.