Question

"Question 3 What is the sum of the measures of the angels of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)

Understanding Quadrilaterals Page 41"

Answer 1

A quadrilateral is a four sides Polygon. It has four angles.

 
Angle Sum Property
Sum of angles of the Quadrilaterals =360º

Convex Polygon
In convex polygons  all the diagonals are inside the Polygon.

Concave Polygon
In concave polygons  all the diagonals are not  inside the Polygon.

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 Solution:
[fig. is in the attachment]

The sum of the measures of the angles of a convex quadrilateral is 360° as a convex quadrilateral is made of two triangles.

In fig.convex quadrilateral, it made of two triangles. Therefore, the sum of all the interior angles of this quadrilateral will be same as the sum of all the interior angles of these two triangles i.e., 180º + 180º = 360º

This property also holds true for a quadrilateral which is not convex. This is because any quadrilateral can be divided into two triangles.

Here again, in the fig concave quadrilateral is  made of two triangles. 

Therefore, sum of all the interior angles of this quadrilateral will also be 180º + 180º = 360º

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Hope this will help you...

Answer 2

Yes , the property will be hold of the quadrilateral is not convex

The explanation of the answer is given below

Hope it will helpful for everyone ☺️