In convex pentagon $ABCDE$, angles $A$, $B$ and $C$ are congruent and angles $D$ and $E$ are congruent. If the measure of angle

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1 year ago

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$A$ is 40 degrees less than the measure of angle $D$, what is the measure of angle $D$

1 answer:

kipiarov [429] · Answer 1 · 2023-11-17T21:15:35+03:00

In a convex pentagon, the measure of angle D is 132°.

<h3>What is convex pentagon?</h3>

If a planar polygon has all the line segments connecting any given pair of its points, it is said to be convex pentagon.

Properties of a Convex Polygon are-

Any polygon whose inner angles are all smaller than 180 degrees is said to be convex.
A concave polygon is one in which at least one of the angles is bigger than 180°.
A convex polygon's diagonals are located inside the polygon.
A polygon is considered convex if the line connecting every pair of its points lies entirely within it.

Calculation for the measure of angle D.

The sum of the interior angles = 540°

Let A, B , C = D - 40

And let E = D

So we have

A + B + C + D + E = 540

(D - 40) + (D - 40) + (D - 40) + D + D = 540

5D - 120 = 540

5D = 660

D = 660 / 5

D = 132°

Therefore, the measure of angle D is 132°.