Question

11. Three angles of a quadrilateral are in the ratio
4:3:5. The difference between the greatest and
the smallest angle is 42°. Find all the four angles
of the quadrilateral.​

Answer 1

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Answer 2

Answer:

${\green{let \: the \: angles \: of \: quadrilateral \: be \: 4x \: 3x \: and \: 5x}}$

${ \pink{ \mathcal{ \: sum \: of \: all \: angles \: of \: quadrilateral \: = 360}}}$

Given :

${ \red{5x - 3x = 42}}$

${ {2x = 42}} \\ x = \frac{42}{2} = 21$

The angles are :

$5x = 5 \times 21 = { \green{105}}\\4x = 4 \times 21 = { \pink{84}}\\3x \: = 3 \times 21 = { \red{6</em></strong><strong><em>3</em></strong><strong><em>}}$

The fourth angle is :

$105 + 84 + 6</em></strong><strong><em>3</em></strong><strong><em> + a = 360 \\ a = 360 - 25</em></strong><strong><em>2</em></strong><strong><em> \: \\ { \red{ \boxed{a = 1</em></strong><strong><em>0</em></strong><strong><em>8</em></strong><strong><em>}}}$

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