# Three angles of a quadrilateral are 54⁰, 116 , 85⁰. Find the measure of the fourth angle.

2
by harshithay

2014-11-23T11:55:17+05:30

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Let the 1st, 2nd, 3rd & 4th angles be a° , b° , c° & d° respectively.

a° = 54°
b° = 116°
c° = 85°
d° = ?

We know the sum of all angles of a quadrilateral is 360°.
According to the problem,
a° + b° + c° + d° = 360°
54° + 116° + 85° + d° = 360°
255° + d° = 360°
d° = 360° - 255°
d° = 105°
Therefore, the measure of the Fourth angle is 105°.
its 105..!!!! just add the given numbers and subtract it from 360..
2014-11-23T12:14:34+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
So sum of angles of quadrilateral is 360°

so let the unknown angel be x

so the other angles are 54° , 116° , 85°

so we have 54° + 116° + 85° + x = 360°

⇒x  = 360° - 255°

⇒x = 105°

so the fourth angle is 105°