The sum of three interior angles of a convex Pentagon is 420°.if the remaining angles are equal how much does each angle measure?

The sum of interior angles of any polygone is:

Sum of angles = (n-1)x180°, where n is the number of sides. For the pentagone n = 5, then Sum of angles of a PENTAGONE = (5-1)x180° = 720°.
Already the sum of 3 angles is 420°, the measure of the 2 remaining one is
720° - 420° = 300°. Since the remaining angles are equal, hence each one will have a measure of 300°/2 = 150°

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facundo3141592 facundo3141592 · Answer 2 · 2022-03-17T14:25:54+01:00

Each one of the remaining angles measures 60°.

How much does each angle measure?

We know that the sum of the interior angles of a closed figure of n sides is given by:

(n - 2)*180°.

A pentagon has 5 sides, so we use n = 5 and we get:

(5 - 2)*180° = 540°

Now we know that 3 angles add up to 420°.

Then the other two angles must add up to:

540° - 420° = 120°

And those two angles are equal, then each one measures:

120°/2 = 60°.

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