Question

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

Answer 1

Given: A convex quadrilateral.

To find: Sum of the measures of the angles of a convex quadrilateral.

Solution:

• Now, we know that the sum of the measures of the angles of a convex quadrilateral is 360° as a convex quadrilateral is made of two triangles.

• Lets consider a parallelogram, In parallelogram, as a convex quadrilateral, it is made up of two triangles.

• Therefore, the sum of all the interior angles of quadrilateral(parallelogram)  will be the same as the sum of all the interior angles of these two triangles

           180º + 180º = 360º

• This property is also true for those quadrilaterals which are not convex.

• The reason behind that is any quadrilateral can be divided into two triangles.

Answer:

                 Sum of the measures of the angles of a convex quadrilateral is 360°.

Answer 2

Answer:

Let ABCD be a convex quadrilateral and BD be one of the diagonal which divide it into △ABD and △BCD.

Now, the sum of the measures of the angles of a convex quadrilateral ABCD.

= the sum of all the interior angles of the

two triangle

= 180° + 180°

= 360°

Yes, the property also hold true for quadrilateral which is not convex.

Let PQRS be a non-convex quadrilateral and QS be one of the diagonal which divide it into △PQS and △QRS.

Now, the sum of the measures od the angles of a non-convex quadrilateral PQRS

= the sum of the interior angles of the two

triangle

= 180° + 180° = 360°.

✌Here is the full & correct answer ✌

☝Hope it's help you☝