Question

What is the sum of 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

$\bold{ \underline{ \red{convex \: quadrilateral}}}$

$\bold{In \: Quadrilateral \: ABCD}$

$\bullet \: { \bold{sum \: of \: the \: angles}}$

$\angle \: A+ {\angle} \: B + { \angle} \: C+ { \angle} \: D$

$\rightarrow{ \bold{lets \: divide \: into \: 2 \: triangles}}$

$\boxed{ \bold{ {\triangle}ABC\: and{ \triangle} \: ADC}}$

$\underline{ \bold{now \: we \: know \: that}}$

$\underline{ \bold{sum \: of \: the \: triangle \: is \: 180{ \degree}}}$

Answer 2

$\huge{ \underline{ \bold{ᴀɴsᴡᴇʀ....{ \heartsuit}}}}$

convexquadrilateral

In Quadrilateral ABCD

sum of the angles

∠A+∠B+∠C+∠D

→lets divide into 2 triangles

△ABCand△ADC

ꜱᴜᴍ ᴏꜰ ᴛʜᴇ ᴛʀɪᴀɴɢʟᴇ ɪꜱ 180°