If three angle of a quadrilateral are 90,100,110 then find the measure of fourth angle

2 thoughts on “If three angle of a quadrilateral are 90,100,110 then find the measure of fourth angle <br />”

1. Answer :–

   • The fourth angle of the quadrilateral is 60°.

   Given :–

   • The three angles of a quadrilateral are 90°, 100° and 110°.

   To find :–

   • The fourth angle of the quadrilateral.

   Step-by-step explanation :–

   Let the fourth angle of the quadrilateral be “x”.

   We know that :–

   [tex] \underline{ \boxed{ \sf Sum \: of \: all \: angles \: in \: a \: quadrilateral = 360^{\circ}}}[/tex]

   Here,

   • First angle = 90°.
   • Second angle = 100°.
   • Third angle = 110°.
   • Fourth angle = x.

   Now,

   • The sum of all these angles must be equal to 360°.

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   Therefore,

   [tex] \longmapsto\tt90^{ \circ} + 100^{ \circ} + 110^{ \circ} + x = 360^{ \circ}[/tex]

   [tex] \longmapsto\tt300^{ \circ} + x = 360^{ \circ}[/tex]

   [tex] \longmapsto\tt x = 360^{ \circ} – 300^{ \circ}[/tex]

   [tex] \longmapsto \overline{\boxed{\tt x = 60^{ \circ}}}[/tex]

   Hence,

   • The fourth angle of the quadrilateral = 60°.

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   Know more :–

   What is a quadrilateral?

   • A quadrilateral is a closed figure which has four sides.

   More formulae :–

   • Perimeter of a quadrilateral = Sum of all sides.

   • Sum of all angles in a quadrilateral = 360°.

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2. Answer:

   60°

   Step-by-step explanation:

   Sum of all angles should be 360°

   So, fourth angle is

   =360°-(90°+100°+110°)

   =360°-300°

   =60°

   Reply