If the angles of quadrilateral are $x, x + 20, 2 x + 45, x + 15$ . Find $x$ .

52

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56

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Solution

The correct option is A $56$
Given: The angles of quadrilateral are $x, x + 20, 2 x + 45, x + 15$

By angle sum property, the sum of all the angles of a quadrilateral is $360^{\circ}$

$x + (x + 20^{\circ}) + (2 x + 45^{\circ}) + (x + 15^{\circ}) = 360^{\circ}$

$⟹$ $5 x + 80^{\circ} = 360^{\circ}$

$⟹$ $5 x = 360^{\circ} - 80^{\circ}$

$⟹$ $5 x = 280^{\circ}$

$⟹$ $x = 56^{\circ}$

Therefore, option $B$ is correct.

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If the angles of quadrilateral are x,x+20,2x+45,x+15. Find x.

The correct option is A 56Given: The angles of quadrilateral are x,x+20,2x+45,x+15By angle sum property, the sum of all the angles of a quadrilateral is 360∘x+(x+20∘)+(2x+45∘)+(x+15∘)=360∘⟹ 5x+80∘=360∘⟹5x=360∘−80∘⟹5x=280∘⟹x=56∘Therefore, option B is correct.

If the angles of quadrilateral are $x, x + 20, 2 x + 45, x + 15$ . Find $x$ .