Question

In convex pentagon $ABCDE$, angles $A$, $B$ and $C$ are congruent and angles $D$ and $E$ are congruent. If the measure of angle $A$ is 40 degrees less than the measure of angle $D$, what is the measure of angle $D$

Answer 1

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

What is convex pentagon?

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°.

To know more about the convex pentagon, here

brainly.com/question/23602298

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