Question 978655



 if the angles of a quadrilateral are in ratio {{{1 : 2 : 3 : 4}}},the sum of the all angles is {{{360}}} (by definition of the sum of all angle in  a quadrilateral}

so, we can find the measure of the four angles:            

Let the common ratio be {{{x}}}.

Then the measure of four angles is {{{1x}}}, {{{2x}}}, {{{3x}}}, {{{4x}}}

We know that the sum of the angles of quadrilateral is {{{360}}}°.

Therefore, {{{x + 2x + 3x + 4x = 360}}}°

⇒ {{{10x = 360}}}°

⇒ {{{x = 360/10}}}

⇒ {{{x = 36}}}

Therefore, {{{1x = 1 * 36 = 36}}}°

{{{2x = 2* 36 = 72}}}°

{{{3x = 3 * 36 = 108}}}°

{{{4x = 4 *36 = 144}}}°

Hence, the measure of the four angles is {{{36}}}°, {{{72}}}°, {{{108}}}°, and {{{144}}}°.