Question

3. 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

Answer:

in quadrilateral ABCD

sum of angles of ABCD= angle A+angle B+angle c+angle D

Lets divide quadrilateral ABCD into two triangles-

∆ABC&∆ADC

now,we know that sum of angles of triangle is 180°

for ∆ABC

angle BAC+angle B + angle BCA=180°.........(1)

For ∆ADC

angle DAC+ angle D +angle DCA = 180°.........(2)

Adding (1)& (2)

angle BAC +angle B + angle BAC +angle DAC + angle D +angle DAC =180°+180°

(angle BAC+ angle DAC)+angle B+ (angle BCA+angle DCA )+ angle D= 360°

so sum of angles of convex quadrilateral =360°

let's try for non-convex quadrilateral

NON CONVEX QUADRILATERAL :

In Quadrilateral ABCD

sum of angles of ABCD= angle A +angle B + angle C + angle D

let's divide quadrilateral ABCD into two triangles- ∆ABC & ∆ADC